The ICARUS collaboration - operating a neutrino detector sitting not far from the OPERA experiment in the underground Laboratori del Gran Sasso in Italy - produced a refutation of the superluminality of neutrinos a while ago. That refutation was based on studying the energy spectrum of the neutrinos in the CNGS beam, coming from CERN through a trip of 700 km under the Earth's crust: superluminal neutrinos should have lost some energy due to electroweak radiation, which was not borne out by the data.

The early analysis was only a partial refutation, because one could conceivably argue that superluminal neutrinos possessed additional properties to make them free of the need to comply with electroweak physics. So one could think that the neutrinos detected by ICARUS were also superluminal, but they had not radiated the energy that ordinary Standard Model particles would have, under the same circumstances.

Now, however, ICARUS puts a tombal stone on the whole business. This comes at a time when OPERA has explained they have additional systematic uncertainties in their timing measurement, which will require more time to be tracked down fully. We obviously do not need to wait for that now, since the ICARUS result is perfectly in line with neutrinos being traveling at the speed of light, as they should. Note, neutrinos are massive, but their mass is so small that the difference with a particle moving at exactly the speed of light in vacuum, with a 700km baseline, cannot be detected with our clocks.

The rewsult is described in the paper produced today in the Cornell Arxiv, 1203.3433. The money plot is the following one:

As you can see, the ICARUS result is as expected clustering at δt near zero (where zero means the arrival time of particles moving at the speed of light), while OPERA stands out as a wrong result. As expected.

Now, if your prior belief were that neutrinos may or may not be superluminal, with 50% chance to each hypothesis, you might argue that the two results above are inconclusive: their statistical power is similar, and so the fact that each agrees with a different hypothesis puts the matter in the "totally undecided" field. So people who have argued that scientists are too enamoured with their prior beliefs (of the correctness of basic theory against extravagant variants) may continue to believe that neutrinos are superluminal, that OPERA is correct, and that the ICARUS result above is the wrong one. But I hope that readers of this blog know better...

Comments

Pity, having a temporal difference to the action of the other particle connected to weak isospin, would have been beautiful. Neutrinos may still have very strong or maximal CP (which therefore implies T, (exception Mirror Matter)) violation, so I strongly believe there is something odd about time and neutrinos. As late as March, I had explanation for the FTL signal and a chronology projection solution for FTL neutrinos, and then nature the witch, came back with this. But despite the lose of the originating experiment, we can't be sure neutrinos are slower than light until we've measured that slowing with some great precision, not easy with current technology.

I consider the succession of negatives followed by positives (even allowing for 0 to be classified as one wants) as "striking" as the succession of positives followed by negatives, so the first number does not count. Then we have three of each. The chance that I get them "ordered" this way is 0.5*0.4*0.25=5%. Nothing mysterious.Cheers,T.

Yes, nothing mysterious. But the chance, at 5%, is still low. I am not saying they haven't proved OPERA wrong - it is impossible to see how ICARUS could have made a mistake that exactly cancels out a superluminal speed. But the clustering of the +ve values toward the end might indicate a general error in the system that causes tof-v to be progressively less over time. ICARUS is essentially a brand-new system on half of the timing front (the fiber optic cable and underground timing). Maybe something is getting worse as the neutrino-detections proceed.

Just in case I wasn't clear, I do think the OPERA case is indeed totally closed. The two experiment results are logically not on par. It is hard to see how an experiment can miss superluminality and end up with a value the speed of light (what possible error can you hypothesize?). It is easy to see how an experiment can see superluminality (or subluminality) where there is none. This isn't based on one result being more plausible; it is just based on the probability one hits exactly the value 'c' as opposed to hitting an arbitrary value different from 'c' because of experimental errors.

ICARUS hasn't mentioned the energy of the neutrinos, but that doesn't matter either. In their second run, OPERA saw superluminality for every detected neutrino, including the ones showing up as muons from the rocks (external events). So their measurement has errors.

Yes, much better, I like this, forgiven that you just couldn't help it to squeeze in a little kick in the last section, this time you have written so that nobody who holds on to other working hypotheses is getting insulted or the feeling that you are ignorant or participate in forced establishment consensus. Like this, science seems reasonable and trustworthy. Everybody in their right mind expected that FTL neutrinos are very likely a systematic error, and see how fast good measurements and explanations came in. There was never any reason to be impatient and misrepresent relativity theory or jump on "refutations" that do not refute anything.

I am simultaneously disappointed & relieved to hear the preliminary verdict. Lorentz invariance now appears safe again after a century, & mod.physics has reaffirmed its most fundamental tenet. If V > C had been confirmed, it would have opened the floodgates to new physics beyond the std.model, something many are aching to see.
Asked what he would think if Eddington's eclipse expedition had found no light deflection, Einstein quipped:" Then I would've been sorry for the dear lord, the theory is correct". `Time' magazine did not name him `Man of the Century' for nothing.
Ironically, the last holdouts are those that posit a massive graviton ~ 10^-33 ev, which would travel a tiny bit slower than light speed. Thus there would be a `gravity speed' but certainly immeasurably slower than C.

Call me naive, or worse, but I would have never imagined that the speed of light could be such a politically loaded subject. Next thing we know, volt-meters will turn out to be weapons of mass destruction.

Thanks Tommaso for the plot, update and for your blogging! I've been reading your blog for a while, but I have never commented until now. I enjoy following your blog, and I learn a lot from it, thanks!

I have followed this stuff from the beginning - and the question I have never quite been able to get answered is - why does everyone keep saying that Einstein's Relativity rules out superluminal particles? The parts of it I understand certainly seem to allow it, even if it requires the rest mass of the particles to be imaginary, but we've seen that before, where the solutions to equations at first glance seem to have no physical realization (Dirac's predictions of antimatter come to mind). Obviously I don't understand relativity however, since I can beat Einstein's windowless room acceleration/gravity equivalence thought experiment with two pendulums.

Of course, my math-fu is weak. I don't even understand how hidden variables (aka unknown particles) has been ruled out with respect to quantum physics in general, since the only reason neutrinos were found in the first place was because the "statistics didn't fit right".

You are correct that "Einstein's [Special] Relativity" does not "rule out superluminal particles". This is something Sascha Vongehr, on this site, has been arguing for quite some time. (Additionally, they actually aren't truly required to have imaginary rest masses, any more than Special Relativity requires time to be imaginary. But that's a whole other discussion that doesn't belong here.)

As for "beat[ing] Einstein's windowless room acceleration/gravity equivalence thought experiment with two pendulums" one must go back to the statement of "Einstein's windowless room acceleration/gravity equivalence thought experiment", in terms of what is meant by things like "local experiments", and a "uniform gravitational field", and such.

Yes, one can detect the non-uniformity of the Earth's gravitational field, and the lack of such for a "windowless room acceleration" experiment in free space, far from any gravitating bodies. However, that's far from the intent of "Einstein's windowless room acceleration/gravity equivalence thought experiment", and far from an appropriate discussion here and now.

As for hidden variables, this is much different than "unknown particles". The reference to "hidden variables" usually harps back to Einstein-Podolski-Rosen (EPR) type experiments, and Bell's Theorem regarding such. It has to do with the inability of local, causal hidden variable theories to match the statistics predicted by, and verified for, Quantum Mechanics.

Well -- apparently not everyone has kept saying so; and some may have been saying so without understanding Einstein's RT firmly enough to keep saying so with conviction.

Those who do, however, apparently understand the thought-experimental principles contained in Einstein's RT on what's meant by (how to measure) "speed";
including the prerequisit definition, attributable to Einstein, and emphasized again especially by J. L. Synge, on what's meant by (how to measure) "distance" of a suitably given source and receiver to each other.

> The parts of it I understand certainly seem to allow it, even if it requires the rest mass of the particles to be imaginary [...]

Oh -- so you're imagining terms or even quantities (which may duly arise in considerations of "dynamics") before you have understood the notions of "distance" and "speed"? ...

So, pretty much the public's entire mis-understanding of relativity is because Einstein pulled a "Clinton" on his definitions? "Distance" is a pretty damned basic concept. Speed is not much more advanced. Velocity is only a *LITTLE* more advanced, as it's a vector instead of a scalar.

You start pulling *THAT* stuff, and it becomes fairly easy to prove that 1=0.

Tara Li wrote (03/19/12 | 09:45 AM):
> So, pretty much the public's entire mis-understanding of relativity is because Einstein pulled a "Clinton" on his definitions?

At least: pretty much the entire understanding of relativity depends on appreciating thought-experimental definitions. As Einstein put it rather memorably and urgently:

The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition [...].
As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and the same applies if I am not a physicist), when I imagine that I am able to attach a meaning to the statement of [an experimental condition or prescription].

There ("Relativity", chap. 8) Einstein wrote specificly about defining what's meant by (how to measure) "simultaneity". But the concept of "distance" (how to judge equality, or how to determine ratios as real number values) would hardly be excluded.
(And worrying about the definition of "definition" or the meaning of "meaning" isn't necessarily "pulling a Beavis & Butthead", IMHO.)

> "Distance" is a pretty damned basic concept.

(That depends on ...)
Sure: there are plenty more elaborate and derived concepts; and there are only few more elementary concepts (within RT).
But clearly (or conventionally) "distance" is not meant to be equal for all pairs of participants, from the outset. Instead it's a quantity to be measured (pair by pair), and thus requires a definition on how to measure.

> Speed is not much more advanced.

(The important point would be, of course, that the notion "speed" is building up on the notion of "distance", and others; not the other way around.)

> Velocity is only a *LITTLE* more advanced, as it's a vector instead of a scalar.

Well -- isn't it always and necessarily "from the sender to the receiver"? ...
(BTW: that's "pulling an Autiero", IIRC :)

(By the way, things like "<blockquote>"-tagging work quite well if you are logged in. Yes, there are some tags that don't work as expected for those that are not logged in. Perhaps this is an oversight that will be fixed some day. In any case, unfortunately, I suspect it is not a high priority fix. There are other "fixes" that have yet to be accomplished, right now.)

While I don't see anything that you have said that is particularly incorrect, you have also said nothing that supports your assertion (referring to Tara's question "why does everyone keep saying that Einstein's Relativity rules out superluminal particles?"):

Well -- apparently not everyone has kept saying so; and some may have been saying so without understanding Einstein's RT firmly enough to keep saying so with conviction.

Those who do, however, apparently understand the thought-experimental principles contained in Einstein's RT on what's meant by (how to measure) "speed";including the prerequisit definition, attributable to Einstein, and emphasized again especially by J. L. Synge, on what's meant by (how to measure) "distance" of a suitably given source and receiver to each other.

By which, presumably, you are asserting that those who understand "Einstein's RT firmly enough" say "with conviction" "that Einstein's Relativity rules out superluminal particles". By which, presumably, you assert that they do so due to a more "correct" "understanding [of] Einstein's RT".

Now, unless this is a mischaracterization of what you are trying to say, I'm sorry to have to burst your bubble, since even the most stringent application of Einstein's definitions for things like "distance", "time", "speed", and "velocity" most certainly does not preclude "superluminal particles". (Of course, even Einstein had trouble with accepting Minkowski spacetime, at first, though he did accept it before too long.)

Presumably Tara Li's question (03/18/12 | 00:50 AM) wasn't just polling whether it is more popular to "keep saying so" (or "keep saying the opposite"), but aimed at getting a defensible derivation (or arguments to reject a particular derivation attempt, or perhaps any such attempt).

> even the most stringent application of Einstein's definitions for things like "distance", "time", "speed", and "velocity" most certainly does not preclude "superluminal particles"

Sure it does, as best as I know how to apply the relevant definitions. Shall we review foremost the "distance" definition of RT (as implied by Einstein and clarified by Synge): ... ?

p.s.
> By the way, things like "<blockquote>"-tagging work quite well if you are logged in.

Since you don't even fully quote my questions, to you, concerning whether, or not, I had correctly characterized your position, nor do you answer said questions, and, further, you go on to challenge me (on "RT"), am I to presume that I correctly characterized your position?

Presumably Tara Li's question (03/18/12 | 00:50 AM) wasn't just polling whether it is more popular to "keep saying so" (or "keep saying the opposite"), but aimed at getting a defensible derivation (or arguments to reject a particular derivation attempt, or perhaps any such attempt).

Well, while I agree that Tara's question "wasn't just polling whether it is more popular to 'keep saying so' (or 'keep saying the opposite')", I would most certainly not presume that Tara's question was "aimed at getting a defensible derivation (or arguments to reject a particular derivation attempt, or perhaps any such attempt)." I base this judgement upon the rest of Tara's post.

However, since Tara did indicate some trepidation and uncertainty in their understanding of Einstein's Special Theory of Relativity (this is what you mean by Einstein's RT, correct?), I would suppose that Tara may be interested in supporting arguments, especially since Tara has now been addressed from opposite sides of this disagreement.

Now, even after my warning, you appear to be "calling me out" with your challenge:

>[quoting me] even the most stringent application of Einstein's definitions for things like "distance", "time", "speed", and "velocity" most certainly does not preclude "superluminal particles"

Sure it does, as best as I know how to apply the relevant definitions. Shall we review foremost the "distance" definition of RT (as implied by Einstein and clarified by Synge): ... ?

OK. You came here, apparently "itching" for a "fight". You appear to be wanting to try out your relativity-foo.

I'll accept your challenge. At least so long as it's OK with Tommaso. After all, this is Tommaso's 'blog.

I promise to be gentle. ;)

We are talking about Einstein's Special Theory of Relativity, correct? Flat Minkowskian spacetime, and all that, right? (I just want to make sure we are both clear on what the "battle ground" is.)

Take your "best shot": Please provide any definition of "distance", and/or any procedure for determining such you want.

David Halliday wrote (up to 03/21/12 | 20:45 PM):
> [...] opposite sides of this disagreement.

That seems gentle enough for me to acknowledge and to persue.

> [...] We are talking about Einstein's Special Theory of Relativity, correct?

Correct -- were talking about identifiable participants ("pitcher A", "catcher B", "projectile P", ...) who observe each other's signals, each judging order or coincidence of their observations;
where A and B are supposed to be members of a set of participants who are and remain rigid to each other
(in the sense following Synge: obtaining constant ratios of their signal round-trip durations among each other)
and moreover, as the "special" condition: who are and remain flat to each other
(in the sense of Synge's "five point curvature meter", i.e. with vanishing Cayley-Menger determinant of these ratios).

(The underlying definition of how to compare durations in the first place is of course a concern of the RT in general.)

> Flat Minkowskian spacetime

If you enjoy sprinkling tuples of real numbers over the setup, either in any arbitrary way, or perhaps in some particular and yet to be defined way -- it won't make any difference to the judgement of order of observations, or to geometric relations of the participants under consideration (such as the ratios of their signal round-trip durations among each other), or to conclusions about the debated "speed" values, will it? So why bother with coordinates, for our purpose.

> (I just want to make sure we are both clear on what the "battle ground" is.)

That seems a service to all readers, and it applies mutually:
We're talking about "speed of a particle", concerning one certain identifiable particle, such as "projectile P" and its (average) speed "while having been passed from pitcher A to catcher B"; not about "phase speed" (such as involving distinct particles being "met by" A and B), right?, and

We're comparing "speed of P while having been passed from A to B" to "speed of light between A and B" for the case that the "refractive index n" determined between the members of the flat set containing A and B has the value 1 throughout the trial(s) under consideration, promise?

Then, considering participants A and B who are rigid and flat to each other (as members of a suitable set of participants) and who (therefore) obtain equal mutual signal round-trip durations throughout the trial, "[ABA] == [BAB]" (using Synge's notation),
the value of "distance" of A and B to each other is
"1/2 c [ABA]",
where "c" is a literal constant (plainly the letter "c". Proceding to the definition of "speed" in terms of such a distance value and a certain duration value, "speed of light" is subsequently obtained as the value "1 c", or for short "c").

Now, presumably, there's no disagreement on the subsequent definition of "speed" (especially which duration goes into the denominator) and how to evaluate the range of values (the codomain) of this quantity as a consequence? ...

To my query as to whether we are to be dealing with "Flat Minkowskian spacetime", you responded with:

If you enjoy sprinkling tuples of real numbers over the setup, either in any arbitrary way, or perhaps in some particular and yet to be defined way -- it won't make any difference to the judgement of order of observations, or to geometric relations of the participants under consideration (such as the ratios of their signal round-trip durations among each other), or to conclusions about the debated "speed" values, will it? So why bother with coordinates, for our purpose.

Who ever said "Flat Minkowskian spacetime" has anything to do with "bother[ing] with coordinates"? If you think that "Flat Minkowskian spacetime" must imply coordinates, or, worse, some particular set of such, then you show an even greater lack of understanding than I had supposed.

... and moreover, as the "special" condition: who are and remain flat to each other(in the sense of Synge's "five point curvature meter", i.e. with vanishing Cayley-Menger determinant of these ratios).

So, it is "flat", but there is yet (at least) one characteristic you have not yet addressed. However, since you are probably assuming this additional characteristic, I won't belabor the issue. On the other hand, I reserve the right to bring this issue up if I find you are violating this characteristic.

Now, depending upon what you actually mean by:

... where A and B are supposed to be members of a set of participants who are and remain rigid to each other(in the sense following Synge: obtaining constant ratios of their signal round-trip durations among each other) ...

I can already foresee problems. For instance, I can conceive of a definition for "obtaining constant ratios of their signal round-trip durations among each other" that will allow A and B to be moving relative to each-other, at constant velocity, which would not seem to adhere to what many would suppose is meant by "are and remain rigid to each other" (emphasis added).

By the aforementioned statement, are you trying to say that "A and B are" not moving relative to "each other"? Even if you were to modify the restriction of "obtaining constant ratios of their signal round-trip durations among each other" to the more stringent statement that both are "obtaining constant [values] of their signal round-trip durations among each other", this still allows for non-inertial motion among these two.

OK. What else ...

You state:

We're talking about "speed of a particle", concerning one certain identifiable particle, such as "projectile P" and its (average) speed "while having been passed from pitcher A to catcher B"; not about "phase speed" (such as involving distinct particles being "met by" A and B), right?

Fair enough. That's as I would expect as well.

You then continue with:

We're comparing "speed of P while having been passed from A to B" to "speed of light between A and B" for the case that the "refractive index n" determined between the members of the flat set containing A and B has the value 1 throughout the trial(s) under consideration, promise?

That's good for me as well.

You then begin the "crux" of the matter with:

Then, considering participants A and B who are rigid and flat to each other (as members of a suitable set of participants) and who (therefore) obtain equal mutual signal round-trip durations throughout the trial, "[ABA] == [BAB]" (using Synge's notation), ...

OK. Hold just a moment. Now you are talking "equal mutual signal round-trip durations", yet, earlier, you were talking about "obtaining constant ratios of their signal round-trip durations among each other" (emphasis added).

Now, I'll go along with [ABA] as a notation for a round-trip light signal duration. No problem there (just need to make it clear that we are talking about a light signal, you know, " 'refractive index n' determined between the members of the flat set containing A and B has the value 1 throughout the trial(s) under consideration", and all that).

I'll even go along with [ABA] == [BAB], so long as we are talking about both A and B undergoing only inertial motion, and that the moment of initiation for these two "round-trip light signal durations" may be completely independent of each-other. In other words, A may initiate A's "round-trip light signal", that has duration [ABA], completely independent of when B initiates B's "round-trip light signal", that has duration [BAB].

Now, I'm reasonably certain I can still prove that Einstein's Special Theory of Relativity does not preclude superluminal particles even without such "quibbles" (because I can do it even within General Relativity with arbitrary observers and non-inertial motions). However, especial for the sake of other readers, I believe it best that we be this specific.

All right, now that that's out of the way...

You go on with stating:

... the value of "distance" of A and B to each other is"1/2 c [ABA]",where "c" is a literal constant (plainly the letter "c". Proceding to the definition of "speed" in terms of such a distance value and a certain duration value, "speed of light" is subsequently obtained as the value "1 c", or for short "c").

I have no problem with this (with the proviso concerning [ABA], and such, already stated.

You then finish off with:

Now, presumably, there's no disagreement on the subsequent definition of "speed" (especially which duration goes into the denominator) and how to evaluate the range of values (the codomain) of this quantity as a consequence? ...

Actually, so far, you don't have a proper "duration [which] goes into the denominator" for anything other than some two-way speed. As for the last part—"how to evaluate the range of values (the codomain) of this quantity [meaning 'speed'] as a consequence"—we shall see...

Sure. Explaining what's meant by "manifold" requires the notion "chart".
(Unless you suppose otherwise; so please correct me if I'm wrong.)
My point regarding manifolds in general and "Flat Minkowskian spacetime" in particular is for our purpose:
"let's not bother with charts" but consider "pitcher A" and "catcher B" (among others) themselves, with their relations, immediately. Otherwise we should have to review "how to make charts", too.

> By the aforementioned statement, are you trying to say that "A and B are" not moving relative to "each other"?

I'd submit that there's an ... appropriate ... definition required for how to measure ... that;
and that I've tried to sketch some level of detail of such a definition ("rigid and flat").

The principles or axioms or standards of appropriateness within RT are (of course) that such definitions presume and use the abilities of all participants to
> > observe each other's signals, each judging order or coincidence of their observations .

In order to resolve our disagreement it may still become necessary to explicitly break down the definitions of "distance" and "speed" to this axiomatic level; but that's quite laborious.
Meanwhile, considering ratios of signal round-trip durations (evaluated for the same participant, or even comparing between distinct participants) may be suitable.

> I can conceive of a definition for "obtaining constant ratios of their signal round-trip durations among each other" that will allow A and B to be moving relative to each-other, at constant velocity, which would not seem to adhere to what many would suppose is meant by "are and remain rigid to each other"

There may be quite a few meanings of "rigidity" (or also of "velocity") to which different people (mean to) adhere (best).
But considering the care of your reading and comments I'd like to amend the "rigid and flat"-definition under consideration for our purpose by the requirement that the flat set containing A and B is not "degenerately flat"; in particular that not all members are (triple-wise) "straight" to each other.

> Now, I'm reasonably certain I can still prove that Einstein's Special Theory of Relativity does not preclude superluminal particles even without such "quibbles" (because I can do it even within General Relativity with arbitrary observers and non-inertial motions).

(Your quibbling is fine; but I'd wonder how to obtain real-valued "speed" ratios without the aforementioned "flatness"-condition or with the participating "ends" being related to each other by quasi-distances, instead of distances.)

> Now, I'll go along with [ABA] as a notation for a round-trip light signal duration. [...]
> I'll even go along with [ABA] == [BAB], so long as we are talking about both A and B undergoing only inertial motion

What's that?? -- How (else) would you define "inertial motion of A and B" in terms of duration ratios involving A, and B (and additional participants as needed)?

> and that the moment of initiation for these two "round-trip light signal durations" may be completely independent of each-other. In other words, A may initiate A's "round-trip light signal", that has duration [ABA], completely independent of when B initiates B's "round-trip light signal", that has duration [BAB].

Right: [ABA_j] == [ABA_k] == [BAB_p] == [BAB_q],
for any pair of distinct initiating indications "A_j" and "A_k" of A and any pair of distinct initiating indications "B_p" and "B_q" of B, throughout the trial under consideration.
(To me this follows from the requirement "rigid and flat throughout".)

> [...] just need to make it clear that we are talking about a light signal

Right -- we're considering signals "as such"; regardless of any possibly accompanying "baggage" (such as "energy", "momentum", "stress", "spin", "charge", ...).
(Perhaps you were thinking of being somehow more specific? Then you might try to be more specific without benefiting from the "distance" notion developed so far ...)

> so far, you don't have a proper "duration [which] goes into the denominator" for anything other than some two-way speed.

"some two-way" what?? (Have we obtained a "speed" definition already??)
Let me better try to be explicit on "the denominator" in any case:
that would surely be the duration of A from its indication of having been met by P to A's indication simultaneous to B's indication of having been met by P;
or equally (due to A and B being members of a flat set) the duration of B from its indication simultaneous to A's indication of having been met by P to B's indication of having met P.

Btw.: do you know or even prefer a notation for those durations, just in case?
Otherwise I'd suggest "[(A|B_P)(A_P)]" and "[(B_P)(B|A_P)]" ...

The "flat set with A and B" can contain a participant as "middle between" A and B, who judges "simultaneity" of A's and B's indications according to the definition of "Relativity, chap. 8".

Even as long as my previous reply was to you, I can see that our exchanges are likely to get even longer, for the next little while. So, in order to help ease reader fatigue, and, hopefully, to help your ability to respond to individual points, since your ability to "blockquote" isn't so great (due to editor limitations), I'm going to split my responses between multiple messages.

Besides, I don't have the time, right now, to respond to very much of your latest message.

To my attempt to explain why I had asked about whether we were dealing with "Flat Minkowski spacetime", wherein I indicated that "coordinates" were not what I was getting at, I tried to redirect by pointing out that " 'Flat Minkowskian spacetime' pertains to a manifold with particular characteristics." Unfortunately, you then gravitated toward "coordinate" related aspects, again, with:

While the simple explanations of "manifold" do work from "chart", it is, essentially, unnecessary, especially in this particular case.

You go on with:

My point regarding manifolds in general and "Flat Minkowskian spacetime" in particular is for our purpose:"let's not bother with charts" but consider "pitcher A" and "catcher B" (among others) themselves, with their relations, immediately. Otherwise we should have to review "how to make charts", too.

Do you not recognize that you have a hidden assumption of a "manifold" of some kind? If you have "points", "objects", "things that exists and interact", you have a "manifold" of some kind.

Do you know how dangerous it is to proceed without even acknowledging hidden assumptions?

OK. Back to "Flat Minkowskian spacetime". Since the manifold is flat, such a manifold can be identified with a real (as in using the real number field) (pseudo-)metric space, where the (pseudo-)metric is Minkowskian. (You do recognize that this means that the space is a [linear] vector space, where the scalars are from the real number field, that has a real Minkowskian [pseudo-]metric. You also do recognize that a vector space needs no coordinates, no "charts", not even a basis, though one is always able to find a basis whenever one may wish, but we don't need such.)

So, is your assumed "manifold" a real (pseudo-) metric space, where the (pseudo-)metric is Minkowskian?

I just noticed that Wikipedia, at least, defines a "Metric Space" as something different than what I was intending (it's because it has a definition for Metric that's different). Now, I wouldn't be surprised if both (differing) definitions are used by different people. In fact, what I was thinking of as a metric space is, indeed, a metric space according to their definition, but my definition includes more axioms and features, so not all of their metric spaces would be my metric spaces. (A similar thing occurs with the definition of a number field. To some, a number field is what others call a number ring, with the second group saying a number field is a number ring that adheres to additional axioms, so not all number rings are their number fields.)

So, in order to find what I was thinking of, one would need to look for "Inner Product Space" in Wikipedia. So, everywhere I used the term "metric" just substitute the term "inner product". That will get what I was thinking of.

... where A and B are supposed to be members of a set of participants who are and remain rigid to each other ...

You still haven't properly address the ill defined nature of this "rigid to each other" phrase.

Your first "definition" was:

in the sense following Synge: obtaining constant ratios of their signal round-trip durations among each other

To which I pointed out that

I can already foresee problems. For instance, I can conceive of a definition for "obtaining constant ratios of their signal round-trip durations among each other" that will allow A and B to be moving relative to each-other, at constant velocity, which would not seem to adhere to what many would suppose is meant by "are and remain rigid to each other" (emphasis added).

To this, you respond by, apparently, simply trying to skirt the issue with:

There may be quite a few meanings of "rigidity" (or also of "velocity") to which different people (mean to) adhere (best).

Not so fast. You were the one that introduced this concept of "rigidity", as in "rigid to each other". It is you that is required to provide a "rigid" (as in rigorous) definition for such.

So far, I have pointed out a number of issues with your supposed "definition": One being the way one can use the above "definition" to "claim" that "A and B ... moving relative to each-other, at constant velocity" satisfies the "definition" of A and B "are and remain rigid to each other", as I did above. Another is the way you later changed the "definition", or simply used something rather loosely related, to claim that these participants (A and B) that "are and remain rigid to each other" (supposedly by the former definition)

Wait a minute. First you said "rigid to each other" meant "constant ratios of their signal round-trip durations among each other" (emphasis added), then you claim an equality.

Additionally, you gave no indication as to whether the initiation of the two durations have any particular relationship.

Fortunately, after I raised this issue and stipulated that I would go along with this equality provided:

the moment of initiation for these two "round-trip light signal durations" may be completely independent of each-other. In other words, A may initiate A's "round-trip light signal", that has duration [ABA], completely independent of when B initiates B's "round-trip light signal", that has duration [BAB].

You now state (where I've taken the "liberty" to translate the TeX subscripting into actual subscripts)

Right: [ABAj] == [ABAk] == [BABp] == [BABq],for any pair of distinct initiating indications "Aj" and "Ak" of A and any pair of distinct initiating indications "Bp" and "Bq" of B, throughout the trial under consideration.

In fact, you then have the "gall" to claim "to me this follows from the requirement 'rigid and flat throughout'." While my expectation of what I would mean by a "requirement" that is labeled as "rigid and flat throughout" does match the above relationship, this relationship most certainly does not follow from your earliest definition.

You need to improve your methods for creating/expressing definitions that actually mean what you want them to mean.

Now, there is one remaining "bugaboo" about the definition of "rigid and flat throughout" that you have yet to properly address.

As I stated along with your first definition:

... Even if you were to modify the restriction of "obtaining constant ratios of their signal round-trip durations among each other" to the more stringent statement that both are "obtaining constant [values] of their signal round-trip durations among each other", this still allows for non-inertial motion among these two [A and B].

I continued along this same vein with my conditional agreement (emphasis added):

I'll even go along with [ABA] == [BAB], so long as we are talking about both A and B undergoing only inertial motion, and that the moment of initiation for these two "round-trip light signal durations" may be completely independent of each-other. In other words, A may initiate A's "round-trip light signal", that has duration [ABA], completely independent of when B initiates B's "round-trip light signal", that has duration [BAB].

Yet, you respond to the bold phrase above with

What's that?? -- How (else) would you define "inertial motion of A and B" in terms of duration ratios involving A, and B (and additional participants as needed)?

Do you not know what "undergoing inertial motion" means? Are you actually trying to say that one cannot specify "undergoing inertial motion" unless one can specify such only "in terms of duration ratios involving A, and B (and additional participants as needed)"?

If you are not at the point of being able to admit the concept of "inertial motion" then you have a long way to go before having well defined "velocities", or even "speeds". You most certainly are not at a point of being able to define "simultaneous" in any self consistent manner (as you appear wont to do, in order to obtain your "definition" of "speed") without being able to define inertial motion.

Perhaps there is something hidden within the vague "definition" of "flat to each other" "in the sense of Synge's 'five point curvature meter', i.e. with vanishing Cayley-Menger determinant of these ratios". Perhaps you need to go into more detail on this. Can this definition of "flat to each other" distinguish between inertial and non-inertial motion? There are myriad ways to distinguish such, I'm just not sure whether this procedure does such.

David

P.S. By the way, it sure seems that this J. L. Synge "character" has you going through a great many convoluted hoops. Why can you not go from Einstein's own, rather straight forward and simple treatise on his own theory? Is it because you know I'm correct from Einstein's own perspective, but, perhaps, the convolutions of this "character" have succeeded at blinding you to the truth behind Einstein's own theory, or, perhaps even worse, has blinded you (and perhaps even himself [we call that delusion]) to some "sleight of hand" substitution for some convoluted non-Einsteinian "RT" in place of Einstein's Special Theory of Relativity?

I don't know, I'm just wondering why you appear to be taking such a convoluted course.

I've looked up Distance Geometry and Cayley-Menger determinants. I've actually done work involving such things, but didn't know such by these names. (I've actually worked out other things involving generalized distances, though I would be hard pressed to find what I did, in any particularly short amount of time.)

Now, in this case, the "five point" or five element Cayley-Menger determinant, that determines "flat", involves the ten (absolute) "distance" measures, not ratios thereof (though one can certainly have any scaling one may wish, but this is not expressed as "ratios of" "distances" or "intervals"). (It also requires that not all quadruples are "plane", and "plane" requires that not all triples are "straight".*)

* So, if this "straight" is the meaning of your "requirement that the flat set containing A and B is not 'degenerately flat'; in particular that not all members are (triple-wise) 'straight' to each other", then this is simply not applicable to our two participants. Even once we add a third "participant", namely "projectile P", this will not be applicable, at least so long as A and B are only undergoing inertial motion. (Now, with the addition of your "participant as 'middle between' A and B", it is certainly possible to have only inertial motion while having this participant not being "straight" with both A and B.)

** I know that one can have points in a hyperbolic (and spherical) geometry that are "flat"/"plane" by that geometry, but that are not "flat"/"plane" by "planar" (Euclidean) geometry. In the case of Minkowski geometry, there are spacial surfaces (having time-like normals) that have hyperbolic geometry. So there may be a connection that may be exploitable there.

To my insistence that we specify that these "signals" that you have going between the participants be specified as light signals (so we have the specificity that they travel at the speed of light in a vacuum, you know, " 'refractive index n' determined between the members of the flat set containing A and B has the value 1 throughout the trial(s) under consideration", and all that), you respond with:

Right -- we're considering signals "as such"; regardless of any possibly accompanying "baggage" (such as "energy", "momentum", "stress", "spin", "charge", ...).(Perhaps you were thinking of being somehow more specific? Then you might try to be more specific without benefiting from the "distance" notion developed so far ...)

Well, you do recognize that there are many forms of "signals", and that many of them do not travel at the "speed of light" in any medium, let alone a vacuum.

Since your definition of "distance" relies so absolutely upon the "speed" of such signals, then it behooves us to be specific about these signals not just being just any kind of signal, but a particular class of signal (we can call it a light signal, or some other "specification" for "signal"). It is in this sense in which we must be "more specific".

Look. I don't know about you, but I can already go from your durations, the "speed" of the "special" signals (call them light, or whatever you will, but they are a specific class of signals, not just some generic signals), the exact same thing you have already used to define "distance", and I can already provide a procedure for determining the (average) "speed" of any other "projectile P" that is "thrown" from "pitcher A" and "caught" by "catcher B" without any need for defining any procedure for determining simultaneity of events that occur at different locations, and without any additional participant "middle between" A and B.

My procedure doesn't involve a convoluted "duration" for the denominator, however, it does involve a very simple duration that one can already obtain from the use of your "special" signals, and the simultaneous emission of such a "special" signal with the "throwing" of "projectile P", by the same participant that "throws" "projectile P". So it only involves simultaneity of events at a single location (single spacetime event), like the flash from a "gun" that launches the "projectile P".

But considering the care of your reading and comments I'd like to amend the "rigid and flat"-definition under consideration for our purpose by the requirement that the flat set containing A and B is not "degenerately flat"; in particular that not all members are (triple-wise) "straight" to each other.

OK. In what sense do you mean "that not all members are (triple-wise) 'straight' to each other"? At this point we have but two members (A and B) at any given "time",* so they cannot help but be "straight" to each other, and there is no "triple-wise", in this sense.

So, you must have some other sense in which these two participants can have "not all members [be] (triple-wise) 'straight' to each other".

Are you trying to stipulate that participants A and B do not occupy the same point in space at any "time"? Or (as a more likely possible interpretation), that they do not occupy any point in space over any non-zero interval of time (so, the "triple-wise" would be any triplet of events, directly associated with these two participants, where no more than two such events are associated with the same participant)?

Yes, you've got more explaining to do here, unless this is all inconsequential.

David

* This is almost completely independent of how one wishes to define any temporal simultaneity, since this is true for any spacetime surface with time-like normals, for time-like participants (tardyons, like you and I).

Incidentally, this does bring up another tacit assumption that I have been making, and I expect you have been as well: The participants A and B are time-like. Of course, this harks back to the Minkowski nature of the manifold (real [pseudo-]metric space with a Minkowskian [pseudo-]metric). Do you know how this relates?

Fine -- let me first address the topic that I find easiest to consider separately, and which may be especially consequential.

> To my insistence that we specify that these "signals" that you have going between the participants be specified as light signals (so we have the specificity that they travel at the speed of light [...]), you respond [...]

Actually I recall having responded to

> > > [...] just need to make it clear that we are talking about a light signal

-- no insistence on signals "travelling" or somesuch.

> "special" signals (call them light, or whatever you will, but they are a specific class of signals, not just some generic signals)

Yet the participants under consideration (A, B, ...) are from the outset as generic as can be, aren't they?

> Well, you do recognize that there are many forms of "signals"

Distinguishable "forms of signals"? In RT?? Surely not from the outset, in the "Part on Geometry and Kinematics".
And even if "forms of signals" may subsequently be distinguished (by notions developed in the "Part on Dynamics", or by accounting for "refractive index" values different from 1) it doesn't preclude working out "Geometry and Kinematics" between generic participants considering generic (i.e. all) signals being exchanged between each other. Signals not burdened or discriminated by additional specifications; light signals.

> Since your definition of "distance" relies so absolutely upon the "speed" of such signals [...]

The "chronometric" definition of "distance" (as it is called by Synge) depends on signals being exchanged, and on the notion "duration" as a measurable quantity. "Speed of light signal exchange" being determined as different from zero is merely a consequence.

Of course we're doing well to make all this explicit. You do realize that resolving our disagreement might boil down to answering the question: "By catching P, did B learn that A had thrown P -- or not?" ...

Now I'll try to cover the remaining topics in ... some ... order:

> another tacit assumption that I have been making, and I expect you have been as well: The participants A and B are time-like.

I've repeatedly mentioned the (generically) presumed or granted ability of each participant to judge order or coincidence of observations collected.
This applies to participant "projectile P" as well.

A distinction between A and B on one hand, and P on the other, arises by the setup stipulation: that A and B are explicitly supposed to observe (non-degenerate) signal roundtrips (for instance between each other), while there is no such requirement for P.

> In what sense do you mean "that not all members are (triple-wise) 'straight' to each other"? At this point we have but two members (A and B)

I've clearly required A and B to be members of a set of suitable participants who determine being flat to each other by determining the Cayley-Menger-determinant(s) of their "signal roundtrip duration" ratios as zero; that's a set of at least 5 members.
"Straightness" is similarly to be decided by evaluating the Cayley-Menger-determinant(s) of their "signal roundtrip duration" ratios obtained between 3 participants.

> Are you trying to stipulate that participants A and B do not occupy the same [...]

I'll accept (for our purpose) the stipulation (good point!) that A and B must not "meet" throughout the trial; and I've used the notion "participants having met each other" already above (03/25/12 | 18:40 PM).
Of course I'd hate admitting "meeting" as a primitive axiomatic notion; so stipulating (as I just did above) that A and B shall find non-degenerate signal roundtrips between each other, throughout the trial, seems more appropriate.
A more appropriate description of the stipulation "B met P", for instance, may be more complicated ...

> [...] point in space [...]

The principal elements of discourse of RT are "participants" (a.k.a. "observers") and their individual "indications" (or "times" or, exemplary, "positions of the small hands of the watches" of participants).

> If you have "points", "objects", "things that exists and interact", you have a "manifold" of some kind.

No: we have a "set"; and considering the generic assumptions about all participants you have a "partially ordered set".

Moreover, there are (values of) "durations" and/or "distances" obtained, at least between members of certain subsets. Thereby we have two "metric spaces" (generally on the same subsets).

The metric space pertaining to "distances" (on the subset containing A and B) is stipulated as "flat" and the metric space pertaining to "durations" (on the same subset containing A and B) is (in some sense) itself "straight" (as you've perhaps been contemplating), and they may (therefore) be combined "the Minkowski way"; so we have a "pseudo-metric space".

Is a (pseudo-)metric space necessarily a manifold?? -- I don't think so.

> You do recognize that this means that the space is a [linear] vector space, where the scalars are from the real number field [...]

Or from a rather sparse subset of the real number field.
(So I shouldn't have questioned "coordinate-tuples being sprinkled on the setup", but "real numbers being sprinkled on various subsets of the setup"?`... &)

> [...] that has a real Minkowskian [pseudo-]metric.

Fine -- a "Minkowskian (pseudo-) Inner Product" may be defined, etc.

> [...] the ill defined nature of this "rigid to each other" phrase.

Meanwhile we've got some notation established to deal with this. (Indices with underscore look better readable on my browser, so please bear with me.)

for natural numbers r and s.
Now, the "flatness" condition may also be expressed in terms of these rational numbers "r/s". Thus a definition for (how to measure) "duration" for evaluating "conditions (1)" is obtained, by which "conditions (2)" imply in turn the immediately observable "conditions (3)".

Still (you may be wondering): didn't (even) Synge consider rather "conditions (1)", with or without "(1c)", instead of "conditions (2)" or even "conditions (3)"?

Yes, apparently; my point in referring to "rigidity in the sense following Synge" (03/22/12 | 18:48 PM) was mostly that this is derived by considering signal roundtrips at all, rather than being taken as axiomatic notion.

> Why can you not go from Einstein's own, rather straight forward and simple treatise on his own theory?

Unfortunately, Einstein's treatises don't seem consistently as straight forward as for instance his "strong" statement I quoted above. In the initial Ann. Phys. 17, 895 (1905), for instance, there are plenty coordinates and references to "rigidity" without definition. And (surprise?) no (explicit) mentioning of "inertial motion" either ...

David Halliday wrote (03/26/12 | 17:12 PM):
> I can already provide a procedure for determining the (average) "speed" of any other "projectile P" that is "thrown" from "pitcher A" and "caught" by "catcher B" without any need for defining any procedure for determining simultaneity [...]

As soon as you introduced your "participants", I was reminded of that exchange.

I thought I had responded to your last message, there. I most definitely remember having read that message.

Maybe I was going to get to it, and "life" got in the way. I don't know.

I'm sorry about not having "wrapped that up".

David

P.S. We have yet to get to where the discussion thread gets so cramped that we "guys" tend to feel the need to start a new thread. Besides, especially when there are multiple threads, it is preferable that a "stub" get placed under the appropriate message, pointing to the relevant "new thread". (To help finish the linking, there should be a link near the beginning of the "new thread" that points back to either the "stub" or the message one is actually replying to.)

Admittedly, I haven't seen this done very often at all, but it would help preserve the threaded structure.

P.P.S. When Derek went to a "new thread", due to the cramped quarters we had gotten ourselves into (far more cramped than you and I are now), we had only a single thread. So it was easy for us to transfer. However, anyone that stumbles upon that "new thread" may wonder "where'd that come from", since they would have to search around to find where the conversation was before that point.

First off, the first part of this reply of yours, up until your statement "Now I'll try to cover the remaining topics in ... some ... order:"*, is more properly associated with my message here, and/or here. I would greatly appreciate it if you would respect the threaded structure of discussions. It might actually help you to stick with a single topic at a time.

It was you, back here, that introduced a "constant" "c" for your "signals" that have "signal round-trip durations" given by the notation "[ABA]", and "[BAB]", and such.

So, do these "signals" have a "speed", or not? Is this "speed" the same regardless of "direction", "location", "motions", etc., or not? Do we have other signals, like chemical signals, sound/vibrational signals, contact "signals" (like a string of "participants" nudging each-other)? Is the passing of a "projectile", such as "projectile P" also a "signal"?

So, it would appear that you either have yourself in a quagmire, or you simply cannot "see" your own assumptions.

I shall await a resolution of this issue before addressing any of the rest of this message, because without nailing such fundamentals as these down, there is no hope of progress.

David

* The other portions of this message, after this point, belong under others of my messages. Again, I would appreciate it if you would respect the threaded structure of discussions.

David Halliday wrote (03/29/12 | 10:09 AM):
> [...] So, do these "signals" have a "speed", or not?

Pairs of participants with relations such as those found involving A and B described above can determine the speed at which they exchanged (generic, light) signals among each other; so, using language loosely, yes: "these signals have a speed" -- of value (equally) "1.0 c" (barring rescaling of distances, and thus of speed values, due to refactive index values determined differing from 1).

> Is this "speed" the same regardless of "direction", "location", "motions", etc., or not?

Every pair obtains this value provided they use the same definitions ("operators") for how to evaluate "speed" (as well as in turn the quantities or relations used in the definitions) and who have collected sufficient and suitable observations to apply these operators. And we're talking about "participants", not "locations".

> Do we have other signals [...]

The word "signals" used in various (perhaps overlapping) senses? ...
Well, we should agree on how to express "signal" in terms of the principal elements of discourse in RT:

Given observers A and B observing each other, and considering indication "A_j" of participant A we have the (first, actual) observation of "A_j" by participant B (contained in B's indication "BA_j"), and B may also have other indications before or after "BA_j".

The pair "A_j and BA_j" pertains to A and B exchanging a signal;
any pair of "A_j and an indication of B other than BA_j" does not.

Such language seems appropriate if the attention is not focussed so much on judging order or coincidence of observations (especially concerning signal round trips) but more on "what (if anything) is being passed or spread around".

So let's call the "participant P" we have considered so far being passed from A to B more specificly a "chemical/pill P".
Do you therefore have any assumptions or particular expectations concerning the "speed" which A and B would determine of P? (Provided they satisfy the conditions required for obtaining a speed value at all.)

> Is the passing of a "projectile", such as "projectile P" also [exchange of] a "signal"?

Or is that ruled out? ...
There is also some thought-experimental idealization involved here: for instance that P is supposedly individually recognizable (as are A and B). And that the relevant observations are readily and completely available (surely different from many "real life situations") so their judgement can be correspondingly thorough and consequential.

p.s.
David Halliday wrote (03/28/12 | 17:27 PM):
> P.S. We have yet to get to where the discussion thread gets so cramped that we "guys" tend to feel the need to start a new thread. Besides, especially when there are multiple threads, it is preferable that a "stub" get placed under the appropriate message, pointing to the relevant "new thread". [...]

I'd like you to carry this out, as you see fit, if and when you post an answer to this comment of mine (which I hope is still readable -- no particularly bulky formulas this time). Meanwhile I'll try to support the tracability of the discussion by quoting and repeating the signature stamp of the (or the latest) comment from which I took the quote(s), as usual.

So, what we have are some special class of "signals", such that: 1) " 'these signals have a speed' -- of value (equally) '1.0 c' (barring rescaling of distances, and thus of speed values, due to refactive index values determined differing from 1)"*; and 2) "Every pair obtains this value provided they use the same definitions ('operators') for how to evaluate 'speed' (as well as in turn the quantities or relations used in the definitions) and who have collected sufficient and suitable observations to apply these operators."**

So, this special class of "signals" is most certainly not "generic". Generic "signals", such as the examples I wrote about, most certainly need not have attributes similar to the specifications of "speed", etc., of the above special class of signals.

You continue with:

... we're talking about "participants", not "locations". ..

So long as your "participants" have non-zero separation, so they are not occupying the same "place" ("location") at the same "time", so their "locations" are not degenerate, then you have "locations". These "locations" need not be associated with "coordinates" or any "label" besides the "fact" that a certain "participant" is occupying said "location", at least at some "time" (such as they themselves may determine, since, after all, they are supposedly able to measure "durations").

You then say (my insertions in bold):

Well, we should agree on how to express [this special class of] "signal" in terms of the principal elements of discourse in RT:

Given observers A and B observing each other, and considering indication "A_j" of participant A we have the (first, actual) observation of "A_j" by participant B (contained in B's indication "BA_j"), and B may also have other indications before or after "BA_j".

The pair "A_j and BA_j" pertains to A and B exchanging a[n instance of this special class of] signal;any pair of "A_j and an indication of B other than BA_j" does not.

By "BAj", do you mean the observation, by B (by way of B having receive said "signal", such as by a detector local to B), of the instance of this special class of "signal" emitted by A at "indication" "Aj"? (By the way, your use of the term "indication" seems like it should be using the Einsteinian term "event". In your case, an event of observation by a particular participant. So long as that's what you mean by the term "indication", I'm OK with it.)

Well, so long as you acknowledge that these are a special class of "signal" we are talking about, not just any "generic" class of signal, such as "chemical signals, sound/vibrational signals, contact 'signals' (like a string of 'participants' nudging each-other)", or "the passing of a 'projectile', such as 'projectile P' ", whose principle characteristics, in all such cases, are that they need not adhere to the characteristics of this special class of "signal".

Continuing, you say:

There is also some thought-experimental idealization involved here: for instance that P is supposedly individually recognizable (as are A and B). And that the relevant observations are readily and completely available (surely different from many "real life situations") so their judgement can be correspondingly thorough and consequential.

So the individual instances of this special class of "signals", and every individual "participant", are all distinguishable. So we are not having to worry about Quantum Mechanical issues related to indistinguishable "particles", or such.

I have no problem with that.

So, how do you wish to designate the spacial class of "signals"? It would be nice to have something shorter than "the special class of signal", but it must be more specific than just "signal", unless you wish to stipulate that there are no other classes of "signal".

David

* Of course. We had already agreed to "refractive index n" with "the value 1 throughout the trial(s) under consideration". There is simply no need to "multiply words" based upon that which we have already agreed upon.

** Of course, since your definition of "distance" is based upon the defined "speed" of this special class of "signals", then any non-pathological determination of "speed" of such special "signals" must, of necessity, yield the same, defined "speed".

... Meanwhile I'll try to support the tracability of the discussion by quoting and repeating the signature stamp of the (or the latest) comment from which I took the quote(s), as usual.

So long as you mean that you will place replies under the respective message to which the reply pertains, and providing HTML links to other messages you wish to reference within any given reply you create, I'm happy.

You can designate these HTML cross links via whatever text you think makes sense. Whether that is by way of "repeating the signature stamp of the [relevant] comment", or something else, that's fine.

By the way, if your quotes are coming from the message you are directly replying to (the one under which your reply should show up) I see no reason to use some "linking" mechanism. I never have.

Now, since you are not logging in, so the Rich Text editor is unavailable to you, I'll provide this template for HTML cross links: <a target="_blank" href="http://../../../quantum_diaries_survivor/icarus_refutes_operas_superluminal_neutrinos_again-88060#comment-X">any text you wish, here</a>

Make sure the greater than and less than signs are the keyboard characters and not the HTML character codes (so not the likes of &gt; or &lt;). Replace "X" by the number at the end of the "Rely to This >>" URL. (The number after the last forward slash.)

You very well may be correct that an "exchange [that is] far cleaner than many exchanges I've seen between Sascha and Lubos" may be "nowhere near as much fun :)". :)However, I hope that it will be better for the learning and edification of the participants and the audience at large.

Well, Lubos and Sascha's exchange about E = MC^2 on Tommasso's blog 'The Higg's Mass in Atomic Mass Units' was very stimulating and educational, I just wish I knew which one was right! Any ideas David or is that too dangerous a mine field for even you to tread? Is Sascha right when he says

Energy is inert, inertia is expressed in terms of mass. Energy is NOT converted into mass ever. Energy can take the form of matter, but the mass is just the inertia of the black box which does not change when the electron and positron inside annihilate.

Or is Lubos right when he says :-

The conversion of one type of mass/energy to another is about moving the values from one term to another term in a particular decomposition of the total mass/energy into pieces....In the LHC rings, the protons are given what every sane person - i.e.. people not including you - call energy. It's obtained from the electric fields that accelerate the charged particles around the ring. The energy of a proton is now 4 TeV per proton. When these protons collide, they may create several or lots of top quarks or Higgs bosons which have the mass of 173 or 125 GeV/c^2....One may talk about "mass" and "energy" as two words for the very same quantity (or the same "kind" of a quantity) and that's how it's pretty much done in physics but those laymen can't swallow this identification - that was really my point....It's a completely standard science language to talk about mass being converted to energy or various forms of energy and vice versa, see e.g. these 2 million pages with preprints:

Could Sascha and Lubos both somehow be right, or is it possible that no one really knows the answer for sure one way or the other yet?

Both are correct, and both are wrong!...The principle way in which they are both wrong is in asserting that their description is the total answer, and that the other's description is what is incorrect.

And what is the principle way that they are both correct David? Can energy be converted into mass or not?

First off, we should recall from Newtonian Mechanics the conservation laws of conservation of energy and momentum: The total of all energy (or momentum) before some interaction (or even a complex set of many interactions) will be the same as the total energy (or momentum) afterward.

Second, also from good old Newtonian Mechanics, is the realization that there are multiple forms of energy: Kinetic (energy of motion), potential (stored mechanical potential to do work, such as potential energy in a stretched or compressed spring, or gravitational potential energy, etc.), chemical, etc. And, furthermore, the fact that the conservation of energy law only holds, in general, if all these myriad forms of energy are treated as equivalent, and added together to give the total energy.

Then comes Einstein's Special Theory of Relativity (SR), and his famous equation (derived therefrom): E = mc2. This indicates that mass is also a "form" of energy.

In a sense, the "crux" of Sascha's and Lubos' arguments both stem from this one equation. Lubos retains the "form of" aspect, while Sascha, founded upon the realization that "c" (the speed of light in a vacuum), that is used in that equation, is "nothing but a conversion factor" between the units we call distance and the units we call time—hence, the c2 is "nothing but a conversion factor" between the units we call "mass" and the units we call "energy"—rightfully sees energy and mass as the same "thing".

So, Sascha is completely correct when he says things like "c is a unit conversion constant, so what E = m c^2 is saying is basically E = m, i.e. they are one and the same". On the other hand, Lubos is well within the correct (historic) physics of accounting all forms of energy as being equivalent, while distinguishing them as being of various "types" or "forms".

The next aspect, again within SR, is the way the separate conservation laws of energy and momentum become merged into a single law of conservation of 4-momentum (energy-momentum). So, the total 4-momentum before will equal the total after any interaction.

Couple this with the SR invariant where the square of the magnitude of the 4-momentum = E2 - p2 = m2 (in units where c=1, so such things don't distract), and one finds that this invariant mass will be the same before and after any interaction.

Now, you might notice that there is a disagreement between the first equation (which is Sascha's E = m, in these units) and this last equation (E2 - p2 = m2), unless p = 0. This is because the first equation is only strictly true when we are at rest with the center of mass (which is defined by the total p = 0), so we often append a zero subscript to that energy (E0), the rest energy.*

However, the second equation has universal applicability. In fact, it is what allows one to compare the mass of a box containing an electron and a positron, to the same box containing the two photons after the electron and positron have annihilated—as Sascha put it "the inertia of the black box which does not change when the electron and positron inside annihilate." Furthermore, while the inertia (inertial mass, or just mass) of the box is "defined" in the rest frame of that box, it is at rest with the center of mass of the box and its contents, so p = 0, and we can once again see E = m.

So, in this sense, the total mass (inertial mass, inertia) of the colliding, high energy protons does not change from before they collide to after they collide and a spray of new massive particles are created. On the other hand, the total mass has changed from the time when we had two protons, nearly at rest with each other, to the point where they have been accelerated to high energy just before the collision: The system has gained mass due to the injection of energy into the system, thus accelerating these two protons to high energy.

So, yes, energy can and has been converted into mass. (Of course, that energy came from some mass somewhere else, whether it came from the Sun loosing some mass, or from chemical reactions loosing some mass, or nuclei in a fission reactor loosing some mass, etc.)

The fact is, even just the absorption of a photon by an atom increases the mass of the (now excited) atom. However, the total mass of the photon plus atom system remains the same before the photon is absorbed to after it is absorbed, even though the invariant ("rest") mass of the photon is zero.

Now, I could go on about how this concept of mass, while great for point particles, or composite objects made of nearly non-interacting point particles, doesn't quite cover things when one goes on to more general systems within General Relativity, and how the 4-momentum (energy-momentum) merges into and is superseded (in a general sense) by the energy-momentum-stress tensor, but I'm sure I have provided more than enough for now.

David

* There is another, deprecated way to reconcile these two equations, by calling the second mass—which is the invariant mass—the "rest" mass (often using a subscript zero, like m0), and considering the first equation to be true in any reference frame. In this case, the first mass is called the "relativistic" mass, or, as Lubos put it, "the relativistically enhanced 'total mass'."

As I say, this is deprecated, and only seems to be "favored" by those that seem to want to preserve E = mc2 at all costs, and not to have it muddied with the likes of a subscript zero on the E, as in E0 = mc2.

However, I, and others, consider it rightfully deprecated due to various forms of confusion and inconsistencies people run into when they carry that concept too far. It's especially bad once one starts to consider General Relativity.

You'll be well advised to put the concept completely out of your mind—to forget I, or anyone, ever mentioned it. ;)

Thank you very much David for all your time and effort explaining this to me. It is very much appreciated.

BTW, you might be interested to know that Sascha and Lubos's debate about E=MC^2 may have inspired my son to switch his university degree from animation to physics. He says that he really enjoys a good argument and no one seems to want to argue with him much about animation, physics was his favourite subject at school :)

That is absolutely fascinating to hear about a positive outcome to "that Sascha and Lubos's debate about E=MC^2". I'm very glad to hear that something good appears to have come from it.

Perhaps I judged them too harshly. :(

Of course, I have noticed (for a very long time, now) that some people shy away from math and science (perhaps especially physics and chemistry) because of a mistaken impression that "we already have a good handle on all that, there is no more 'frontier' there".

I have seen many students become far more interested once they recognized that there is yet a great deal we don't know, and there are still new frontiers to be explored.

I would say that our school systems have a tendency to present math and science more like a collection of "facts" than as the dynamic systems they are. I think that is a disservice to the students, and, perhaps even to the disciplines themselves.

No, Helen, it is not possible that no-one knows the answer. Lubos and Sascha both know the physics perfectly well - as does any undergraduate.

Sascha is nit-picking about the correct use of simple terms amongst physicists, Lubos is talking about getting the basic physics across to laymen. They are both 100% right, there is no "somehow" about it. But what better opportunity for them to have a dog-fight about nothing, hamming it up with well-phrased savage invective for the delectation of their devoted audience?

Yes. All "great fun" this "dog-fight about nothing" for those of us that do "know the physics perfectly well".

However, the problem is that there are far more readers here that don't "know the physics perfectly well", as Helen illustrates. I just don't see that such "entertainment" helps such members of our audience.

Perhaps those few that actually "step up to the plate" and either ask direct questions, like Helen did, or even "challenge" those of us that do "know the physics perfectly well", as Frank has, do, ultimately, benefit. But otherwise, not so much.

Helen's asked the same question three times now. Whilst it is fairly obvious that the two crabby sociopaths were not attempting to educate the hoi polloi during their exchange, I am pretty sure that those who "step up to the plate" would be better served by getting a straightforward answer from you than having to endure a second round of arguments about the merits or otherwise of Sascha and Lubos' histrionic extravaganza. As for me, don't try to blame whatever it is you object to onto me, I only offered a round of applause after the show was over.

Frankly I think your reply is over-technical. The key to the copnfusion is that the concepts of mass and energy were defined in the days before relativity. So although we now understand them to be the same "stuff", the layperson may very well attach meaning to converting one to the other, indeed Lubos takes this loose use of language as perfectly normal even amongst scientists. Unfortunately when a pedantic physicist says "they cannot be converted into each other" it is not because classical mass can't be converted to and from classical energy, it's because, to the physicist, they are both the same stuff anyway, just different forms.

It's certainly possible that my reply to Helen is overly technical, as well as being simply too detailed.

On the other hand, even though "to the physicist, they [mass and energy] are both the same stuff anyway, just different forms", does not preclude a valid conceptualization of mass (or matter) and energy being "converted into each other" any more than how kinetic, potential, and chemical energy are all "the same stuff anyway, just different forms", precludes such from being "converted into each other". (This is part of the reason I answered Helen the way I did.)

Unfortunately, in physics we do have a number of different mass "thingies" (at least one of which has been deprecated, by most in relativistic physics): Inertial mass, gravitational mass, rest mass, invariant mass, "dynamical" or "dynamic" mass, relativistic mass, etc. Some of these "thingies" are identified with others, at least within the frameworks of certain theories. However, even when certain theories tag more than one of these as being identical, we physicists must maintain a certain degree of skepticism: Sufficient, at least, to allow for testing the degree of equivalence.

So, perhaps this subject simply isn't as simple as one may suppose, even for one that "knows the physics perfectly well".

On the other hand, even though "to the physicist, they [mass and energy] are both the same stuff anyway, just different forms", does not preclude a valid conceptualization of mass (or matter) and energy being "converted into each other"

There's no "on the other hand" about it. That is precisely what I just said and you all but quoted:

So although we now understand them to be the same "stuff", the layperson may very well attach meaning to converting one to the other, indeed Lubos takes this loose use of language as perfectly normal even amongst scientists.

So, perhaps this subject simply isn't as simple as one may suppose, even for one that "knows the physics perfectly well".

Of course the subject is not simple. The question raised here is simple.

So, do you agree that it is perfectly reasonable for physicists (like me) to talk about conversion of energy from one form to another, just as we have done for centuries?*

Furthermore, since we now (for over a century) understand mass to be one of those forms of energy, that it is perfectly reasonable for physicists (like me) to talk about converting other forms of energy to and from mass?

If so, then you are absolutely correct that there is no "on the other hand". In this sense, as well, the answer to "the question raised here is simple", as long as people can come to understand it this way.

David

* Within the context of General Relativity, gravitational potential energy is an ill-defined, and not a truly applicable concept, so I avoid it as much as I can. We also recognize that, at least in a certain sense, the "gravitational field" (the curvature of spacetime) has "energy" (energy-momentum-stress) associated with it. However, at least at this point, that "energy" is also not so well defined (certainly not localizable, as in how much is at any particular point in spacetime), though in a very different sense than with gravitational potential energy.

It certainly looks like case closed on FTL neutrinos - however OPERA and other labs that have committed to a retest before summer should still do so. Also, I find no mention of the energies of the 7 detected neutrinos in the latest ICARUS paper. Considering that the first part of the paper mentions the energy range of several past experiments and given the level of detail in TABLE 1 for each of the 7 events, the fact that the energy of the detected neutrinos is absent is a little suprising and annoying. However, until I find out otherwise I assume ICARUS, like OPERA, detected muon-neutrinos in the 20 to 40 GeV range.

I'd certainly like to see the re-tests. For one thing, as I understand it, the OPERA setup identified at least two sources of error - one of which would have resulted in reporting the neutrinos as slower than they were. We've got two sources of error that could contribute, and so many seem to be jumping from "could" to "did". After all, this is the second experimental setup that has shown superluminal neutrinos, and I never saw any comments about anyone actually confirming any sources of error in the MINOS experiment (though it was only a 1.7 sigma detection). In fact, this article: http://blog.vixra.org/2011/09/19/can-neutrinos-be-superluminal/gives a graph (http://vixra.files.wordpress.com/2011/09/betadecay.png) where, of 16 measurements of m^2(v)c^4, 15 result in a negative value, though the error bars all allow for a zero or positive value.

All of this strongly suggests that there is something going on, and we need more study.

There are a great many experiments where the likelihood of observing anything inconsistent with present theory is quite slim (to nearly none). However, since we are talking science, rather than something else, it is, nonetheless, quite important that such "lost cause" experiments are performed.

Even though such experiments usually only yield ever tightening bounds around present theoretical predictions, such refinements are an important part in our pursuit of truth and reality.

If we ever stop such pursuits, you can be sure that we have stopped doing science.

I have read the ICARUS paper Arxiv, 1203.3433, but I can't see any mention about the measured neutrino energy which is quite important data in the experiment. And compared to OPERA paper, this ICARUS paper is poorly written. It seems that more complete paper is needed for a better comparison with OPERA. And also, as a scientist, we'd better think that at least one of OPERA and ICARUS might be wrong but there is no scientific reason to give more credits to the later experiment. We need to wait until May for a final decision.

I have read the ICARUS paper Arxiv, 1203.3433, but I can't see any mention about the measured neutrino energy which is quite important data in the experiment. And compared to OPERA paper, this ICARUS paper is poorly written. It seems that more complete paper is needed for a better comparison with OPERA. And also, as a scientist, we'd better think that at least one of OPERA and ICARUS might be wrong but there is no scientific reason to give more credits to the later experiment. We need to wait until May for a final decision.

So, do you agree that it is perfectly reasonable for physicists (like me) to talk about conversion of energy from one form to another, just as we have done for centuries?Furthermore, since we now (for over a century) understand mass to be one of those forms of energy, that it is perfectly reasonable for physicists (like me) to talk about converting other forms of energy to and from mass?

Well you may understand mass to be one of those forms of energy, I understand mass and energy to be essentially the same stuff. <sarcasm>Of course you are a physicist whereas I am a layman.</sarcasm>

One could split an already split hair - using the logical principle of trichotomy :) - and say that the actual identity of energy and mass is not proven and probably not provable, but equivalence is taken to be absolute. Thus all energy has mass. Or is mass. It doesn't make sense to talk of converting other forms of stuff that has mass into mass nor other forms of mass into mass.

However, it may not make proper sense but of course it is still perfectly reasonable to do so! It's just that the language is a bit loose. What is possibly more to the point is that generally, when one refers to conversion into mass, one means conversion of other forms of energy into matter, thus reverting to the classical concepts where mass is measured in bags of cement and energy is measured in terms of how much electricity Wales uses in a fortnight. Unfortunately the distinction between energy and matter is not crystal-clear either: not if one believes in virtual particles carrying all those energy fields :)

I do query the wisdom of using language loosely. If you mean matter, say "matter". No-one says "What's the mass with you?" when I'm being even more cantankerous than usual: why should physicists have special licence to use words sloppily?

I had an idea for a "massless" drive for a spaceship, though I decided it would not work.But, take a positron and an electron and accelerate them down a long accelerator that was split into 2 lanes, one for electrons, and one for positrons (there by creating a force on the accelerator which was really the ship itself).At the end of the accelerator, allow them to collide and annihilate, creating gamma rays. Direct the gamma rays back to the start of the accelerator lanes and impact into some material that would create a positron and an electron, which you'd feed back into the accelerator. And you'd have a drive that didn't consume propellant.But I decided that the gammas would generate an opposite force to the drive, making it work as if you blew on a sail to make a sailboat go, ie it wouldn't work.

I decided that all of the net forces would cancel out, but maybe I was being too rash.What if you had a reflector at the back (annihilation) end that reflected the gammas back to the front, would that counteract the gammas colliding into the front where the electrons and positron are generated? Plus there would be (I would think) a force from the electrons/positrons springing away from the source as well.

As long as there was a slight positive force, you could make a drive out of it. But boy would it need a lot of energy to make work.....

And yes, I do realize there are a number of required technologies that it'd have to have which don't exist (and may never exist)....

Remember, force equals the time rate of change of momentum, so if momentum isn't going out away from you, then your momentum can't be increasing in the opposite direction.

While you recognize that the electrons and positrons have momentum (momentum that you are increasing as you are accelerating them), you seem to be neglecting the fact that the gamma rays created when they annihilate carry the same momentum (conservation of momentum).

If you reflect the gamma rays toward the front, they have the opposite momentum, so the reflector must have received twice the momentum as the gamma rays originally had (conservation of momentum, again).

Now, the interesting thing is that whatever it is that carried the momentum out the back does not have to be matter, like rocket exhaust. It can be light (gamma rays), or even gravitational waves.

Did you know that two spinning* black holes can merge into a single black hole, but in such a way that they emit such a large burst of gravitational waves in one direction that the resulting black hole gets a large kick in the opposite direction?

This was actually found first using computer simulations of black hole mergers. At first, the researchers actually thought they had something wrong with their computer code! But when they looked more closely, and noticed the gravitational waves that were emitted, they realized they had no mistake, everything was working as it should.

Then, more recently, astronomers have found some compact objects, that look like they are almost certainly black holes, moving at very high velocity relative to any nearby galaxies. They think they may have actually seen the results of such a merger.

David

* Since practically everything we observe out in space is spinning/rotating, it makes sense that black holes are more likely to be spinning than not.

Thank you David,I was hoping, but I already had a good idea you'd say this. Yeah, bummer. As for beaming gammas out the back, I would guess that you'd be able to get as much or more thrust pushing matter, which would mean you'd have to replenish the matter at at some point. Which was the point of my "massless" drive. Oh well........I guess we'll just have to wait for a warp drive.

This was actually found first using computer simulations of black hole mergers. At first, the researchers actually thought they had something wrong with their computer code!

I spend about 15 years supporting electronic circuit simulators, and you'd be surprised (or not) at how often simulators give answers that aren't what's expected, and there is a bit of art figuring out if it's a real answer, an artifact of the model, or the question you've asked. I had one such experience where I had to help figure this out, but I wasn't allowed to see the circuit in question, fun, fun.

Since practically everything we observe out in space is spinning/rotating, it makes sense that black holes are more likely to be spinning than not.

I would think that since almost everything grows by accretion (or collisions), and momentum is conserved, most black holes have very high rates of spin, and pulsars would seem to in general confirm this.

Some black holes, that we have been able to measure their spin, do, indeed, spin at "very high rates". In fact, they appear to be spinning at very nearly there maximum rate (the rate of the extreme Kerr solution, for which any higher spin will no longer have an intact event horizon [there are "proofs" that one cannot get past this point by transferring angular momentum via in-falling matter]).

However, there are some black holes that appear to be spinning in the opposite direction to their accretion disk. These would not get spun-up by the in-falling matter, they would tend to get spun-down. On the other hand, I have read some research that suggests that these may be the black holes with the greatest jets (matter escaping from the poles of the black hole)!

(The research also suggests that the easiest way to determine whether a black hole is spinning in the same direction as its accretion disk, vs. the opposite direction, is to look for the size of the gap between the inner edge of the accretion disk and the event horizon of the black hole: The black holes that spin opposite to their accretion disks will have the largest gap.)

I've collected some "Black Hole" web pages from the Astronomy Picture of the Day (APoD). Though I wasn't able to find my favorite (an illustration/model), I hope I found some that might be of interest to you.

Check out these:

Too Close to a Black Hole http://apod.nasa.gov/apod/ap101207.htmlToo Close to a Black Hole http://apod.nasa.gov/apod/ap020908.htmlToo Close to a Black Hole http://apod.nasa.gov/apod/ap001210.htmlToo Close to a Black Hole http://apod.nasa.gov/apod/ap970105.htmlToo Close to a Black Hole http://apod.nasa.gov/apod/ap951127.html

At the Center of the Milky Way http://apod.nasa.gov/apod/ap051023.htmlSgr A*: Fast Stars Near the Galactic Center http://apod.nasa.gov/apod/ap070114.htmlSgr A*: Fast Stars Near the Galactic Center http://apod.nasa.gov/apod/ap001220.html

The ones that are grouped together are highly related, or have the same picture. If they have the same name, they will not necessarily have the same picture, and even if they do have the same picture, the accompanying story may or may not be the same. (It does appear that someone at APoD was very enamored by "GRO J1655-40: Evidence for a Spinning Black Hole", and "Too Close to a Black Hole", however.)

In better images some of these galaxies do show some gravitational lensing, but it's hard to see here.It really need more exposure time, but I have to work around the weather, the moon and the time of year. And in fact NGC4438 shows a bubble from an active black hole, but it's not really visible in my photo.

And I'm limited to visible light, because my camera is limited to visible light :)Plus it's hard to do x-ray astrophotography from my driveway.

So, now I think I understand: What you were looking for was a nearby black hole (or black hole candidate) that you would be able to photograph yourself.

I like your desire. Unfortunately, at least so far as we know, there are no particularly nearby black holes (or even candidates). (It could sure help our understanding of how General Relativity and Quantum Mechanics should be combined, if we could find a nice, friendly, nearby black hole. ;) )

However, there are some places within our galaxy that do have black holes, or at least good candidates, that one could get a visible light image of: The center of our galaxy (though that, of course, would just look like a picture of the Milky Way), Cygnus X-1 (near the Cyg. OB3 cluster), and V404 Cygni.

You could look (in astronomical catalogs, or other literature) for other binary star systems that have black hole candidates as the unseen partner.

:)but I'm glad you mentioned both X-1 and V404, as I was thinking they were below the horizon, but I've taken lots of images in Cygnus, and it will be in the sky shortly.I'll have to see if I can get to the milky ways center.

I am not at all referring to "using language loosely", let alone "sloppily". Science has enough difficulty with things without being loose with the language. In fact, science usually uses language in a far more rigorous manner (often to the confusion of the lay public, because we are using terms that "sound like" common terms in uncommon ways*).

What I am referring to is a rigorous recognition of the different forms of energy, just as we physicists have done for centuries. Do you consider kinetic energy to be the same as potential energy as the same as chemical energy, even though they are forms of the same stuff (or, as you put it, in the case of mass and energy, "essentially the same stuff" [emphasis added])?

Now, if energy, in all its forms, also always had mass, then you would be quite correct that there would be no useful distinction between energy in the form of mass, and other forms of energy. The trouble is that not all forms of energy have mass! (In a sense, at least within the context of Special Relativity, all bound forms of energy have mass [in the form of total invariant or "dynamic" mass], but not all forms of energy are bound.)

David

* I am most certainly not referring to "color"/"colour", "charm", "strange", "up", "down", "top" (I preferred "truth"), "bottom" (I preferred "beauty"), and such cases where physicists have gotten "creative" in their application of "common" words as new "labels". No, I'm referring to the way physicists understand both "acceleration" and "deceleration" to simply be acceleration, and how they (we) make a distinction between mass and weight, and talk about energy in cases where the general public "sees" no "energy".

Instead of asking me whether I consider different kinds of energy "the same" when I had just said I don't think it can be proved, why don't you come to the point and explain what you meant by "The trouble is that not all forms of energy have mass!"

Could you please give an example? I presume this will come from GR which means I won't be able to make an intelligent comment. Nevertheless can you please explain how such energy can be converted into mass?

Instead of asking me whether I consider different kinds of energy "the same" when I had just said I don't think it can be proved, why don't you come to the point and explain what you meant by "The trouble is that not all forms of energy have mass!"

Could you please give an example? I presume this will come from GR which means I won't be able to make an intelligent comment. Nevertheless can you please explain how such energy can be converted into mass?

Wow. I never would have guessed that you didn't already know this. Honest, the thought never occurred to me.

I used it, above, in my reply to Mi Cro: Light, in fact anything that moves at the speed of light in a vacuum (like "gluons" for the Strong Nuclear "force", and neutrinos, back when we thought they were massless), is massless, it has no mass, no rest mass, no invariant mass. Yet, of course, light (in the form of gamma rays) is what is given off when an electron and positron annihilate (this process can also be reversed), and light being absorbed by an atom (creating an excited atom) is the example I gave Helen.

Wow. I never would have guessed that you didn't already know this. Honest, the thought never occurred to me.

Good, because it is not true. I suggested GR precisely because I know perfectly well about the cases you mention and that you couldn't possibly be meaning them as you'd be wrong. I'll say it again then. All energy has mass.

You are making great play of a particle's invariant mass being zero, but that is not what "energy has mass" means. It means inertial mass. You can measure it by changes in momentum when photons make elastic collisions.

When photons make elastic collisions, it is not strictly inertial mass you are "seeing". What you are seeing is conservation of energy and momentum, or, more properly, conservation of 4-momentum. (Incidentally, 4-momentum, for any time-like particle [so, moving at less than the speed of light] is exactly proportional to the 4-velocity of that particle, and, other than a unit conversion factor of some appropriate power of c [the power is determined by what units one uses for 4-momentum aka energy-momentum], the proportionality is given exactly by the invariant/rest mass of the particle.*)

Now, if you attempt to look at this case from a Newtonian perspective, then you will get a kind of "inertial mass" usually called "relativistic mass". This is the deprecated "form" of "mass" that I referred to earlier.

While one can use "relativistic mass" to (almost) preserve the forms of Newtonian mechanics, one also finds there are cases where one ends up with different "masses" for different directions of interaction with a relativistic particle. This is only one of the inconsistencies that lead to the deprecation of this concept.

Once one goes on into the realm of General Relativity (not actually going fulling into the Theory, but sort of the way many lay people try to "think about it") one finds that this "relativistic mass" leads to incorrect "intuitions" concerning gravitational interactions, and the "gravity" of a relativistic particle.

Going fully into General Relativity puts the final nail in the coffin of "relativistic mass". It simply has no place, and violates Einstein's general covariance/invariance principle (while invariant/rest mass transforms as a scalar, so there is no need for such to be determined by dynamics, "relativistic mass" transforms as the "time" component of a 4-vector, so it doesn't have a meaning on its own, and whatever 4-vector it is the "time" component of must be determined through dynamics**).

So, if you wish to reside among those that cling to this deprecated concept of "relativistic mass", that's fine. However, I will not be a part of that. I will not play that game.

David

* This is actually even true for "particles" that travel a greater than the speed of light (call them whatever you may wish). In fact, even for such faster than light (FTL) particles, the "mass" for the proportionality is still real (and positive), not imaginary! The only type of particles for which this doesn't work out so well are particles that have no finite 4-velocity, namely light-like particles. For these, one obtains the improper infinity times zero. Light-like particles are always massless, whether they are photons, "gluons", or even the hypothetical "graviton".

** As the energy-momentum (4-momentum) 4-vector, we see where the dynamics come in, but this simply obviates any "need" for this concept of a "relativistic mass".

Oh boy! You could have said all that at the beginning and saved a load of confusion. How many times do I have to remind you, I am not a physicist? I have never needed to look into 4-momentum. On the other hand, your apparent delight in tripping people up warns me that you could easily be misrepresenting the matter deliberately.

The longitudinal mass and the transverse mass are different if defined in terms of acceleration under a force because Newton's 2nd law: f=d/dt(mv) requires both derivatives: v.dm/dt and ma. So my example of measuring the relativistic mass by collisions is more trouble than it's worth. Fair enough.

However, to get back to the point, I still don't understand your (David's) assertion that not all forms of energy have mass. We've ruled out a simple matter of terminology, restricting mass to the invariant mass. It's relativistic mass we're talking about otherwise the point is trivial.

I have pointed out that "relativistic mass" is a deprecated concept for quite some time. I most certainly do not "delight in tripping people up", let alone "misrepresenting [any] matter deliberately". However, I was most certainly beginning to wonder whether you were working from the (deprecated) concept of "relativistic mass".

As you say, "It's relativistic mass we're talking about otherwise the point is trivial." Since "relativistic mass", as you say, "is more trouble than it's worth" (hence the reason it is a deprecated concept), the "point is trivial": All "forms of energy" that are light-like are massless.

Now, as I pointed out with Helen (most certainly not a physicist), there are cases where we combine massless forms of energy (and even massive forms of energy, like high energy protons, where the rest mass is small compared to the energy involved) in ways where the invariant mass of the entire system is non-zero (or far larger than the sum of the rest masses [rest mass equals invariant mass for individual particles]), and since the invariant mass (as its name should imply) does not change, even through complex interactions, we see a combined energy, even from such "forms", that does yield massive matter as a result of interaction.

As I tried to point out, when one goes on to consider gravitational interaction (whether semi-Newtonian like, or fully General Relativistic), the deprecated concept of "relativistic mass" becomes far worse than "more trouble than it's worth"—it becomes downright misleading. All the more reason why the concept is deprecated.

I apologize if you feel like I "tripped you up". It was most certainly not my intention. I have been completely consistent in my assertions, and my use of the language of physics. (Talk about using language in a way that is far from "loose" or "sloppy", but in a highly rigorous manner, and, yet, causing the lay public difficulty in understanding.:( )

As you say, "It's relativistic mass we're talking about otherwise the point is trivial." Since "relativistic mass", as you say, "is more trouble than it's worth" (hence the reason it is a deprecated concept), the "point is trivial": All "forms of energy" that are light-like are massless.

are just jousting with words. For a start, I did not say "relativistic mass is more trouble than it's worth, I said "my example of measuring the relativistic mass by collisions is more trouble than it's worth".

It's quite important because I said several cycles back

You are making great play of a particle's invariant mass being zero, but that is not what "energy has mass" means. It means inertial mass. You can measure it by changes in momentum when photons make elastic collisions.

For the reasons I have said, direct measurement of inertia doesn't work, so the example is poor. Nevertheless the reason why, as you say

one also finds there are cases where one ends up with different "masses" for different directions of interaction with a relativistic particle

is trivial:f = dp/dt = d/dt (mrv) = mr.dv/dt + v. dmr/dtSo the solution is: don't ignore the force required to give the newly added relativistic mass its momentum. Not rocket science (well it probably is rocket science actually.) So we need to measure the inertial relativistic mass transversely if we want to get it without other terms. The centripetal force needed to keep protons in their curved paths in an accelerator would be directly relevant. I'd be amazed if they don't measure it routinely at CERN (it's always CERN). Go on, tell me it doesn't relate to E=mc2! I do not know of any other reason relativistic mass is deprecated outside of GR. Even if it turns out to be impossible to measure the transverse inertial mass of uncharged particles, it still doesn't matter - it's no worse than inferring the "rest mass" of a photon when, as far as we know, they never come to rest. But there may be other reasons it isn't liked.

I actually don't have a problem with dp/dt, and having to take into account any time rate of change of whatever "mass" may be a part of the momentum term, p.

Actually, I was hoping that you were actually admitting that "relativistic mass" "is more trouble than it's worth". However, I certainly recognized that you may well have meant the more narrow "my example of measuring the relativistic mass by collisions is more trouble than it's worth". (I know the latter is literally what you said, I was just hoping...)

Well, at least you're still willing to ask for further examples, and arguments as to why one "should" deprecate the concept of "relativistic mass".

Now, as far as "inferring the 'rest mass' of a photon": 1) this is a simple matter of taking the energy and momentum, that one can measure, and applying the relationship E2 - p2 = m2 (in units where c=1)—the equation for obtaining the rest mass of any single particle, or the invariant mass of any system of many particles (including only a single particle); 2) if photons, or any "force" carriers, have any mass, they have different force/potential characteristics, and different quantum statistics—for instance, if photons (the electromagnetic field) were not massless, the Coulomb law would not be an inverse square law (it would have and exponential decay multiplier).

Back a few years, when the scientific community was celebrating Einstein's "miracle year", I remember some good discussion of why E = mc2 (Einstein's most famous equation) is more rightly expressed as E0 = mc2, since the only m ever used in all of physics is rest/invariant mass, never (anymore) "relativistic mass", and why the concept of "relativistic mass" (that would make the former equation "always" applicable) was a "bad idea" (why it was deprecated).

I'll see if I can relocate such. Otherwise, I'll have to "wing it", since I never even think in terms of "relativistic mass".

Oh, as for

... The centripetal force needed to keep protons in their curved paths in an accelerator would be directly relevant. I'd be amazed if they don't measure it routinely at CERN (it's always CERN). ...

For a charged particle traveling at constant speed around a circle in a constant, uniform magnetic field, the radius of the circle is proportional to the momentum of the particle divided by the product of the particle's charge and the strength of the magnetic field. So, for any given type of particle (so the charge is known, such as a proton), the magnetic field simply needs to be adjusted based upon the particle's momentum, in order to keep it going around the same circle.

Again, no need to look at "relativistic mass", just momentum.

Now, admittedly, the rate at which it will go around the circle will depend on the particle's speed, so the period will be the circumference of the circle divided by its speed. This speed is equal to the momentum (times c2) divided by the total (relativistic) energy of the particle.

So we only need the components of the 4-momentum (aka energy-momentum 4-vector). (The fact is, from the known rest mass of the particle, we can calculate both the momentum and total energy from the circumference of the circle and the period of the motion of the particle around it. These are the things that are the easiest to measure as a particle circulates around a known circle.)

Again, no need for the "relativistic mass". However, as I pointed out earlier, the time component of the 4-momentum, the total (relativistic) energy, is what used to also be called the "relativistic mass" (times c2). So one can look at it that way, if one really wants to.

Actually, I was hoping that you were actually admitting that "relativistic mass" "is more trouble than it's worth". However, I certainly recognized that you may well have meant the more narrow "my example of measuring the relativistic mass by collisions is more trouble than it's worth".

The clue would be that I said the one thing and not the other. You misquoted me.

Well, at least you're still willing to ask for further examples, and arguments as to why one "should" deprecate the concept of "relativistic mass".

Yes and I haven't seen any forthcoming from you yet. I don't know why you should say "at least". I am more than willing to unlearn outdated ideas and adopt better ones. However what I said is true - I only know of the one objection to relativistic mass and it's easily dealt with.

Now, as far as "inferring the 'rest mass' of a photon" ...

Yes I know about how you calculate it. You've missed the point again. Rest mass is a crazy idea for photons that are never at rest. But we calculate it exactly the same way as we calculate it for massive particles - not by direct measurement. So there is no need to worry about the fact we can't always measure relativistic mass directly. That was all.

The force needed in all accelerators, that are used these days, naturally balances out for all relativistic characteristics. After all, the magnetic field is just a relativistic transformation on an electric field.
So, no, "relativistic mass" doesn't show up there, either.

No, that cannot possibly be true. The centripetal force has nothing to do with the type of deflecting field. The exact same reaction is felt by the apparatus that creates the field. Ultimately, the bolts in the floor push the LHC proton beam inwards to the middle of the ring regardless of whether the deflection is mediated by magnetic fields, electrostatic, or a portable black hole.

You may want to take a look at the version of my message that you actually replied to. You'll notice I had already reconsidered my words.

Honest, I did not change it after you posted your reply (as the dates and times will verify). I don't have such privileges, under someone else's blog.

However, you do bring up an important point, about the stresses placed upon the accelerator itself. I was so focused upon the interaction between the charged particles and the electromagnetic field, I didn't even let my mind wander out to that level.

However, even if we ignore the energy and momentum radiated away by the electromagnetic field in the vicinity of the accelerator (the most important of which is the synchrotron radiation, due to forcing the protons to curve), the reaction is not about inertial mass, as it is about changing momentum.

Now, this brings up the single most important issue. One that both you and Sascha have brought up, before, but one we have not fully addressed. (I blame myself. :( )

I was thinking about these things last night, when I was trying to sleep.

Let's try a different tactic. As you (mostly) correctly state, below, "this discussion is not about the merits or otherwise of the concept of relativistic mass, it's about whether 'all energy has mass' - even if, for that to make sense, we are obliged to hold our noses and play the deprecated game!"

The only thing I would add or modify with the above statement is the question of what mass we are talking about when trying to answer the question of whether or not "all energy has mass". As both you and Sascha have pointed out, before, the only mass of true consequence, in such a question, is "inertial mass". So the question becomes whether or not "all energy has" "inertial mass".

I wish I had thought to take this approach much earlier. I'm very sorry I didn't think of it back then. I got too focused on the wrong (for this discussion) aspects. (Part of the problem, I suppose, is my fully internalized knowledge of what the answer is. I'm essentially "blinded" by my own knowledge.)

OK. So the first question we must resolve is: What is inertial mass? Of course, in a certain philosophical sense, this is a very difficult (maybe even impossible) question to actually answer. However, we can approach this from a more practical, pragmatic, and operational standpoint: Where do we see inertial mass in the equations of physics/mechanics/etc.?

Ignoring the potentially thorny issue of whether gravitational mass and inertial mass are equivalent or the same (and ignoring Quantum Mechanics, which has its own way of looking at such matters), isn't the primary, if not only place where we see inertial mass within mechanics (including interactions between charged particles and electromagnetic fields) good old Newton's F = ma? (Yes, I know, this is more generally and more correctly expressed as F = dp/dt. However, I wanted to make the appearance of the inertial mass as explicit as possible.)

In other words, the resistance to acceleration, due to an external force.

OK. That was all well and good for low speed, low energy applications, but what is the equivalent equation when we are talking relativistic mechanics. After all, that's where we even introduce the possibility that the mass (maybe inertial mass) of a particle might actually depend upon the reference frame one is using to refer to such.

Now, rather than me simply pulling the answer "out of the hat", so to speak, I would like to know if you know what the relativistic form of this equation is.

So, do you know, or can you "hazard a guess" as to what the relativistic form of F = ma = dp/dt is? (If so, of course, please be my guest and share it with us all.)

You may want to take a look at the version of my message that you actually replied to.t You'll notice I had already reconsidered my words.Honest, I did not change it after you posted your reply (as the dates and times will verify). I don't have such privileges, under someone else's blog.

<shrug> I dare say I was composing my reply for some time, during which you probably amended your post. These things happen.

However, even if we ignore the energy and momentum radiated away by the electromagnetic field in the vicinity of the accelerator (the most important of which is the synchrotron radiation, due to forcing the protons to curve), the reaction is not about inertial mass, as it is about changing momentum.

Feel free to include the synchrotron radiation. Don't forget, the LHC, for example, uses protons not electrons, and synchrotron radiation is inversely proportional to the fourth power of the rest mass. This was one of the serious doubts raised about whether the thing would ever work, there would not be enough synchrotron radiation to damp the beam. The actual radiation is a few kW of mostly hard ultraviolet IIRC. As the centripetal force is ~ 1A bending through ~10T I suppose there's a few newtons per metre all round the ring. The synchrotron radiation force must be negligible in comparison. If it were electrons it would be another matter - by 17 orders of magnitude

I was thinking about these things last night, when I was trying to sleep...

Now, this brings up the single most important issue. One that both you and Sascha have brought up, before, but one we have not fully addressed. (I blame myself. :( )

... So the question becomes whether or not "all energy has" "inertial mass".

I get nervouswhen I hear my name bracketed with Sascha. I'm sure he feels the same way. However as for the question being "whether all energy has inertial mass" you should not have lost any sleep over it, it has always been the plain meaning. But in case it was not obvious, several cycles back I reminded you that "several cycles back I said "... it means inertial mass". That's two nested "several cycles back". I keep on saying it.

In other words, the resistance to acceleration, due to an external force. ... Now, rather than me simply pulling the answer "out of the hat", so to speak, I would like to know if you know what the relativistic form of this equation is. So, do you know, or can you "hazard a guess" as to what the relativistic form of F = ma = dp/dt is? (If so, of course, please be my guestand share it with us all.)

I withdraw my apology. You *are* out to trip me up!

I would "hazard" F = mrel.a . Or F = m0.a if you prefer. However F =ma is not the only measured forceunless you apply the force laterally to avoid changing
.

This isn't getting anywhere. Do hurry up with those disasters that ensure when we talk about relativistoc mass, I was hoping to learn something. :P)

Incidentally, your earlier equation with F = dp/dt, where p = mrel v is the closest, so far. If we say that Newton's equation, where we use m0 (the rest mass), rather than mrel, is a zeroth order approximation, your F = dp/dt, where p = mrel v is a reasonable first order approximation.

However, would you believe that for a particle like object (so it moves as a small "solid" object) the actual relativistic equation is F = dp/dτ, where τ is the proper time for the particle like object, F and p are 4-vectors, rather than the 3-vectors of Newton's equation, and p is the 4-momentum (aka energy-momentum 4-vector), where p = m0u, where u is the 4-velocity?

There is one additional stipulation, due to the nature of the 4-velocity: p⋅F = 0, where the inner product is the natural Minkowskian inner product. This comes from the fact that for τ to be the proper time, for the particle like object, u⋅u = 1, always. So 0 = d(u⋅u)/dτ = 2u⋅du/dτ.

If you want to check, you'll see that it reduces to the Newtonian case when velocities are much much less than the speed of light. It is the only choice available (of any of the equations presented here, so far) that transforms appropriately for Lorentzian transformations.

We can even obtain the correct force, F, for a charged particle interacting with an electromagnetic field, if you want.

I most certainly wasn't trying to "trip you up".You could certainly simply say you don't know.

Phooey! Your question was deliberately vague and, as usual, you are harping on the wrong thing.

We are talking about the usefulness of "relativistic mass" as a concept, now refined to mean inertial mass. We are not talking about 4-vectors. Well, you are, but so far what you've said has been uniformly irrelevant.

Newton's 2nd law is based on false assumptions. However it does speak of things which are measurable in the observer's frame: such as force, the observer's time, acceleration. Thus the correct, relativistic, form is simply the relationship between F, m and a with the right assumptions. This permits an operational definition of mass

On the other hand, we do not measure 4-force, we do not measure proper time. I am delighted that F=dp/dτ in relativity just as it does in Newtonian mechanics - once we re-define F, p and t (τ) . But the elegant simplicy of p/dτ=F counts for nothing if none of the quantities can be measured.

I did not make my question "deliberately vague". However, I intentionally tried hard not to have my question be too "leading". I wanted you to feel free to provide any form you felt to be most appropriate. I wanted you to be able to provide any answer you would feel most comfortable with. I didn't want you to feel like I was pushing you into an answer you obviously don't want.

So I'm sorry you feel it was too vague.

As for whether we measure 4-vectors. We do it all the time. It's just that when one is working from a Newtonian perspective we think of these as separate 3-vectors and another "scalar" like entity, like energy, spacial displacement vs. time, etc.

From the 3-vector velocity, we are always able to determine the "time" component of the 4-velocity, and the proper time interval. From the energy and the momentum we have the 4-momentum. From the 3-vector force, we can obtain an approximation, at least, to the 4-vector force. We also always have the ability to obtain the rest mass (the invariant mass).

If the system we are observing is "clock like", then proper time is directly observable. In fact, these "pesky" subatomic particles (and atoms) actually require us to pay attention to proper time—it is the only time that has any real meaning when we are trying to understand what they are doing, and what is happening (such as particle and excited atomic state decay).

Everything is there. We simply have to loose ourselves from the bonds of Newtonian Mechanics, and, even more importantly, Newtonian thinking.

The fact is that all forces we humans directly experience are either gravity or electromagnetic in character. While, as Einstein found, bringing gravity into a relativistic form requires a further change in our thinking, electromagnetic forces are already in a relativistic form. In fact, the simplest and most natural way to express electromagnetic forces yields a 4-force, and one that, completely naturally, satisfies the additional condition p⋅F = 0.

You had said that "this discussion is not about the merits or otherwise of the concept of relativistic mass, it's about whether 'all energy has mass' - even if, for that to make sense, we are obliged to hold our noses and play the deprecated game!" And, as you still admit, the question of what "mass" is meant when asking the question of whether "all energy has mass" is, indeed, whether said mass is inertial mass.

Now you're going back on yourself and claiming that (emphasis added) "We are talking about the usefulness of 'relativistic mass' as a concept, now refined to mean inertial mass."

Isn't a question of "usefulness" a question of "merits or otherwise"?

I have shown that in the full relativistic treatment, the mass that plays the role of inertial mass, completely analogous to Newton's inertial mass, is the rest mass (the invariant mass), and not the "relativistic mass".

[Additionally, I have already shown that there is no actual utility to the concept of "relativistic mass", since, as the "time" component of a 4-vector (the energy-momentum 4-vector, aka 4-momentum), it has no separate utility.]

Another way to approach this issue, though one that is more difficult to fully resolve one way or another, is to ask the question: How does the Newtonian inertial mass transform into different observers' frames?

Part of the problem is that we know "perfectly well" what inertial mass "means"/"is" when velocities are much much less than the velocity of light, but we have so very little experience with velocities that are very near the velocity of light (except for these tiny, miniscule little particles that don't even obey "sensible" rules like Newtonian Mechanics).

There are but two possible answers: 1) it transforms as a scalar (the rest mass, invariant mass), or 2) it transforms as the "time" component of a 4-vector (the "relativistic mass"). These two are completely related to one-another by the fact that the 4-vector that the "relativistic mass" is the "time" component of is p = m0u, where u is the 4-velocity.

This reminds me of a similar, though far more difficult issue: How does Temperature transform into different observers' frames?

There have, historically been three answers to that one:

Temperature is a form of energy (isn't it?), with Boltzmann's constant (k) being nothing but a conversion factor between the units of temperature and the units of energy. So, just like so many other forms of energy, it must transform as the "time" component of an energy-momentum 4-vector. So, a system/object with non-zero temperature must appear to have a higher temperature if it is moving relative to the observer.

Temperature is a measure of internal motions of a system/object. These motions, relative to the system/object, do not change just because it is moving at high speed relative to some observer. However, the proper time of this moving system/object will be observed as slower than the observer's (proper) time. So, the internal motions of this system/object will appear to be slower to any observer moving at high speed relative to the system/object. Therefore, the temperature will be lower. In fact, one finds, from this perspective, that the inverse of the temperature (1/(kT)) transforms as the "time" component of a 4-vector.

The temperature (or kT) of a system/object is independent of the observer's motion relative to that system/object. Temperature (or kT) is an invariant scalar. In this way, whether one needs to look at it as a form of energy (like inertial mass), or if one needs to divide something by this quantity (so multiply by 1/(kT)), there is never a problem, because it is simply a scalar.

Since we still have yet to develop a fully Relativistic Thermodynamics/Statistical-Mechanics (in fact, many of the aspects of Thermodynamics/Statistical-Mechanics are quite incompatible with relativity, even the modern Bose-Einstein and Fermi-Dirac statistical distributions), this issue has been debated for the past century, or so, with little if any resolution.

In fact, attempts to use black-body radiation as a means to resolve this conundrum has been to little, if any avail. The fact is, this yields contradictory answers, since as a black-body moves toward an observer (or, equivalently, the observer moves toward it) the temperature measured in this way is seen to be higher than at rest with the black-body. However, as the same black-body continues past the observer (or, equivalently, the observer continues past the black-body) the temperature measured, in the very same way, is seen to be lower than at rest with the black-body.

However, I read a rather interesting recent paper on this issue. (I was looking to see what progress has occurred toward a Relativistic Thermodynamics/Statistical-Mechanics.)

In that paper, they carefully looked at all the Thermodynamics/Statistical-Mechanics equations involving temperature (really always in the form of kT, of course), and how those equations would transform when transforming between reference frames (as much as possible, to the best approximation they could).

Their conclusion was that one always had equations where either the temperature transformed as a scalar, or the temperature was paired with the average 4-velocity of the system (u) as u/(kT). So, one can either consider temperature to transform as a scalar, or its inverse as the "time" component of the 4-vector u/(kT).

Of course, either way one looks at this, one finds that this form of energy does not transform as the "time" component of an energy-momentum 4-vector.

Of course, for both the question of temperature and inertial mass, by far the simplest and most flexible approach is to treat these as scalars, since then there is never any problem applying any power of such. Trying to use a "time" component of a 4-vector always has more restrictive applicability, due to the nature of its transformational requirements.

So, you are free to use "relativistic mass", that transforms as the "time" component of an energy-momentum 4-vector, and "relativistic temperature", whose inverse (1/(kT)) transforms as the "time" component of a different kind of 4-vector (so the "mass" of this form of energy is sort of an inverse temperature—that sure seems odd that this "mass" should increase as temperature decreases [becoming infinite as temperature goes to absolute zero]). However, they will prove increasingly difficult to use as problems become increasingly complex.

Actually, upon a little reflection on what I have already written about the deprecation of "relativistic mass", perhaps the single greatest reason for the deprecation of that concept, besides just the trouble it does cause, is the simple fact that it provides nothing that cannot be handled quite simply without it.

Yes, the "time" component of the energy-momentum 4-vector (aka 4-momentum) is what used to be called the "relativistic mass" (times c2), but that gains us nothing that cannot already be done by simply using the 4-momentum anyway.*

Just a passing thought.

David

* Along with this, the concept of the 4-velocity (which is proportional to the 4-momentum, using the rest mass) already relates directly with "velocity, as we know it" based upon the "slope of the path in spacetime" (see, for example, Johannes Koelman's "Velocity: Stuff That Just Doesn't Add Up"), so the ratio of the spacial components to the time component, in whatever coordinate system we are concerned with.

I'm certainly interested to learn what all this "trouble" is that you keep hinting at but never reveal. However, this discussion is not about the merits or otherwise of the concept of relativistic mass, it's about whether "all energy has mass" - even if, for that to make sense, we are obliged to hold our noses and play the deprecated game!

Thanks Derek, so why do they call the Higg's boson the God particle? If all energy already has mass then there's nothing particularly amazing about the Higg's mechanism is there? Why all the 10 billion dollar fuss?

The Higgs mechanism and the Higgs boson are related but not the same thing. The Higgs mechanism is (yet another) particle interaction - in this case with a hypothetical backgound Higgs field. This interaction involves energy and thus accounts for some of the mass of some particles, which would otherwise be a mystery. The Higgs boson is the particle associated with the field.

Amazing or otherwise, it would round off The Standard Model - and, no doubt, reveal our next level of ignorance.

It's role in the early universe was a little more dramatic. The Higgs field we live in now could be likened to the solidified lava after a volcano has erupted. The God particle was responsible for the eruption itself :)

At some point after the initial fluctuation, the state of the vacuum was only just stable, with a huge amount of energy available in the Higgs field. This then fell to a lower energy level, releasing the excess energy and, for reasons that are not altogether obvious, :) blowing space up like a balloon.

So in that early epoch, it was basically making the universe as we know it. Hence its nickname.

Unlike other versions of the deity it was not creating it ex nihilo but was converting the energy of "empty" space which was already there.

I think that's worth spending a few billion on. It's only paper money, printed to order...

Well if at high energy/density/gravity(?) our 3 space dimensions are collapsed(like all the other ones that supposedly exist), and you give them a place to expand, instant(well near instant) inflation.

If you say so. My knowledge of cosmology is limited to what I glean from superficially reading articles intended for the scientifically literate layman. If you understand the dynamics I bow to your superior knowledge. I wonder if you could explain to me why our three space dimensions are collapsed at high energies and what this actually means: how would you measure a collapsed meter for instance? Wouldn't you need a collapsed tape measure? And where was this "place" for the "dimensions" to expand? I don't understand how you can have places without the dimensions. Was this "place" something like a big heap of "points" with no particular "positions" until the dimensions expanded and stretched them out? And why would they do that anyway? The only other example I know of very high gravity is a black hole, where instead of expanding, everything collapses - why does it happen one way one time and the other way the other time? You're confusing me.

David - Helen had asked some reasonable questions and wasn't getting any answers. I vaguely remembered a very old Sci Am article. As I have said, I do not know any cosmology worth talking about so I should probably have had a bimble round the web to get up to speed. If you think it will help Helen please go ahead and explain the God particle. It might help me too.

Other than the ambiguous phrase "the state of the vacuum was only just stable"*, and the possibly incorrect attribution of inflation to this transition in the Higgs field (which you pointed out as a possibility in a later message), I thought, and still think, you did quite a fine job. :)

David

* Unfortunately, you also admit that this was not meant to stand in for a more correct description pertaining to the transition from a stable, symmetric equilibrium, to an unstable equilibrium "with a huge amount of energy available in the Higgs field."

Yes, "Helen had asked some reasonable questions", and I had already told both Helen and Mi that I felt it best that you and I finish our discussion of whether all forms of energy "has/is" mass, rather than having our dispute spill over into Helen's questions.

Unfortunately, you then went and spread your outdated/outmoded concept (involving the deprecated concept of "relativistic mass") in your answer to her question. However, I remained silent, because I still didn't want our dispute to spill over. (I didn't know you were going to be so "obstinate" ;) , so we still have no real resolution. :( By the way, why have you not even commented on my last message on the subject? The further one gets from simple mechanical systems with few particles, the more one finds "relativistic mass" to be untenable, even long before going to General Relativity.*)

Of course, your answer, involving the deprecated "relativistic mass" concept, caused Helen some (understandable) difficulty, thus leading to her question concerning the labeling of the Higgs boson as the "God particle". (Of course, I've never liked that label, but you did a fine job of making a good case for something akin to such a moniker.)

David

* Of course, I can even show how the concept of "relativistic mass" is a mistake born from an improper pairing of gamma with the one-and-only inertial mass—which is the rest mass—if you need me to. ;)

Of course, your answer, involving the deprecated "relativistic mass" concept, caused Helen some (understandable) difficulty, thus leading to her question concerning the labeling of the Higgs boson as the "God particle".

Helen - is this true? Would you have understood better if I had told you that not all energy has mass? I have started correcting my original replies as they were all wrong.

Of course, I cannot know with any degree of certainty what Helen actually thought, so I would amend what I said with "appears to have caused Helen some (understandable) difficulty", since all I can go by is what I see.

So, it's certainly good to check to see what Helen actually thought, or found troubling.

The Higgs mechanism and the Higgs boson are related but not the same thing. The Higgs mechanism is (yet another) particle interaction - in this case with a hypothetical backgound Higgs field. This interaction involves energy and thus accounts for some of the mass of some particles, which would otherwise be a mystery. The Higgs boson is the particle associated with the field.

Derek, can you explain what you mean by 'some of the mass of some of the particles, which would otherwise be a mystery' please? Also, is it possible to explain where this all fits in with the periodic table and the 92 naturally occurring elements in the universe and the ways that we know that these were created by the Higg's mechanism either during or immediately after the 'big bang' then later in stars and super novae fusions and explosions etc?

Why are they looking for the Higg's boson or particle at certain positions within the periodic table? I watched one of Professor Brian Cox's DVD's explaining the history of the universe and he likened the 'big bang' and the immediate creation of hydrogen then helium initially by the Higg's mecahanism or field at the bottom of the periodic table to the condensation of symmetrical formless steam onto a frozen glass sheet and the ice crystals that then formed there from the steam like energy of vacuum space. Where does the Higg's mechanism and Higg's field fit into this analogy, is it either the frozen glass sheet or the force behind the frozen glass sheet maybe and why didn't the Higgs boson come before hydrogen and helium atoms on the periodic table?

Derek, can you explain what you mean by 'some of the mass of some of the particles, which would otherwise be a mystery' please?

I shall have a go. Someone (naming no names) can always correct me.

Particles interact with each other - electrons have electric charge and repel each other for instance. This means that whenever particles are brought together there is energy associated with the system - the work done to bring them together. This energy has/is mass. Composite particles, for example the protons and neutrons (not neutrinos, quite different!) which make up more than 99% of all ordinary matter, gain most of their mass this way. Truly fundamental particles do not: by definition they act as single particle systems so there is no energy binding the system together.

DigressionActually there is interaction with their own fields but the simplistic mathematics, far from giving the right mass, actually gives meaningless infinities. Eventually a kludge was discovered: some infinities could be made positive and some negative so they were cancelled, much to the disgust of Paul Dirac who said "Sensible mathematics involves neglecting a quantity when it is small - not neglecting it just because it is infinitely great and you do not want it!" It took a long time but eventually the process, called renormalization, was put on a sound mathematical basis.

For our purposes, the free particle doesn't interact with itself to provide energy. So where does its mass come from? This is where the Higgs field comes in. All of space is assumed to be filled with this field and the particles gain potential energy as a result. Imagine a rubber duck which would be quite happy to sit on the table all day, finding itself forced under water. The bouyancy is a result of the energy needed to submerge the thing. The truly fundamantal particles can have zero bare mass and still end up massive because they are submerged in the Higgs field. The main difference is that the Higgs field is a scalar - it has no particular direction so there's no force on the particles, just energy. Another picture sometimes given is of the particles moving through a honey-like bath of Higgs' particles (and other stuff). These stick to the particle "giving it mass". That doesn't make a lot of sense but I think it means that there is energy holding the Higgs's to the electron. Unfortunately, the picture is terribly misleading as people immediately think of the bulk properties of the honey, which, of course would slow the object down very quickly and nothing in the universe would ever be able to move. Fortunately we do not live in a universe full of honey.

Another DigressionThe electromagnetic field of an electron comprises virtual photons. Photons do not feel the Higgs field and are massless. The strong force - between quarks in a nucleon - is carried by a handful of different partricles called gluons. Glue is an understatement. The forces holding a proton together are said to be around 15 tons. Unlike photons, the gluons feel the Higgs field and are extremely massive.

One particularly important correction (besides any issue of whether all forms of "energy has/is mass"): Gluons, just like photons, "do not feel the Higgs field and are massless."*

David

* See, even you admit that photons are massless. So, not all forms of "energy has/is mass". However, as I have pointed out long before, even these massless forms of energy, when bound into a (time like) system, like Sascha's box or a particle, will contribute to the rest mass of the system, by way of its contribution to the invariant mass (of the system).

P.S. I very much enjoyed the article you linked to (other than his "relativistic mass" slip |-( , he should know better as a more recent graduate [though it appears that he is probably an experimentalist ;) , so I suppose he can be forgiven this slip ;) ]).

Gluons, just like photons, "do not feel the Higgs field and are massless."

Oops, my bad. I'm surprised no-one else pounced.

See, even you admit that photons are massless. So, not all forms of "energy has/is mass"

Now you are being silly.

I very much enjoyed the article you linked to (other than his "relativistic mass" slip |-( , he should know better as a more recent graduate [though it appears that he is probably an experimentalist ;) , so I suppose he can be forgiven this slip ;) ]).

Or perhaps it wasn't a slip and the concept is not quite so deprecated as you would make out.

Oh yes I am very familiar with this. I have been involved in a project which was delayed by approximately a year because the guy running the software development was a purist and refused to use any code that had a GOTO in it.

Also, is it possible to explain where this all fits in with the periodic table and the 92 naturally occurring elements in the universe and the ways that we know that these were created by the Higg's mechanism either during or immediately after the 'big bang' then later in stars and super novae fusions and explosions etc?

What idiot told you that the elements were created by the Higgs mechanism? The Higgs mechanism gives the fundamental particles mass. Nothing to do with nucleosynthesis. At the end of inflation (previously thought to be due to the Higgs particle but now thought to be due to some other mystery particle called an inflaton) i.e. ~ 1^-32 seconds it was all over bar the shouting: the universe was full of fundamental particles - quarks and electrons - but the temperature was too hot for them to stick together

Eventually (okay, it was ~ a microsecond) the quarks joined up to produce protons and neutrons.

After a few minutes it is "cool" enough for nuclear fusion to occur - I know we have difficulty getting up to the temperature for fusion but here we are talking about stupidly high temperatures that rip nuclei apart. For about 17 minutes nuclei crash into each other - but by far the biggest product is helium. Helium nuclei, that is.

After 377000 years (!) the universe has cooled enough for atoms to form.

It's only when stars have formed that nucleosynthesis resumes, now fusing hydrogen to produce helium and in the later stages making heavier elements the same way.

Why are they looking for the Higg's boson or particle at certain positions within the periodic table?

They are not. This is another "helpful" illustration that doesn't quite cut it. The mass of subatomic particles is usually quoted in electron-volts. An electron-volt is exactly what it sounds like, the energy that an electron gains or loses in a 1 volt electric circuit - though you won't catch a physicist talking about electric circuits, they talk about differences in potential of an electric field...Anyway, the electron-volt is a measure of energy and thus mass. As usual the conversion is E=mc^2 so it's not difficult - I'd say that most people have heard of E= mc^2 even if they don't understand it, which is more than can be said of what follows. But electron-volts as a unit of mass is deemed to be too difficult for normal human beings to grasp. So instead of just calling the mass "woggles" or some such meaningless term, our avuncular physicists have gone looking for simple homely units that everyone understands. What better than an atom? It just so happens that the mass of a proton - the simplest atomic nucleus possible, that of hydrogen, is 0.938 or as physicists say, 1, GeV. (This becomes quite accurate for small values of one.) And the heaviest atoms weigh in at about 260 times this. That's convenient because the Higgs appears to be about 125 GeV, slap bang in the middle. So they have dusted off ancient wall posters showing the periodic table of the elements and pored over them looking for atoms that weigh in at about 125 GeV - isotopes with an atomic mass of 133.

That's all there is to it. Just people trying to dumb things down for the hoi polloi. Personally I doubt very much whether the mass of an iodine 133 atom is going to mean anything to anyone: most people will think they're talking about an antiseptic. Tin 133 is unlikely to be any more helpful. I can already hear people asking: "Are they expecting to find the Higgs particle in a tin?"

I suppose the LHC could be described as a tin.

I watched one of Professor Brian Cox's DVD's explaining the history of the universe and he likened the 'big bang' and the immediate creation of hydrogen then helium initially by the Higg's mecahanism or field at the bottom of the periodic table to the condensation of symmetrical formless steam onto a frozen glass sheet and the ice crystals that then formed there from the steam like energy of vacuum space. Where does the Higg's mechanism and Higg's field fit into this analogy, is it either the frozen glass sheet or the force behind the frozen glass sheet maybe and why didn't the Higgs boson come before hydrogen and helium atoms on the periodic table?

This is one of the reasons I intensely dislike Brian Cox.

I've said why the Higgs and nucleosynthesis are nothing to do with each other. The freezing analogy is a simple picture of the role of the Higgs in one, now apparently obsolete, version of inflation. Or maybe the picture was given without a Higgs, just an anonymous "inflaton"?

Anyway freezing etc is a phase change - the molecules spontaneously arrange themselves into a rigid structure as the temperature drops. But forget rigidity, it's the fact that the molecules take up a different and perfectly well-defined relationship with each other. The whateveritwas-on field is supposed to have different possible arrangements and the inflation mechanism would be the field rearranging itself - I have no idea why this would cause the universe to inflate.

Beyond that - let someone who knows what they're talking about take over. I have to go.

I wouldn't, quite, characterize "the role of the Higgs" as being "[with]in one, now apparently obsolete, version of inflation." Basically, as far as I know, the role of the Higgs mechanism in the electroweak symmetry breaking has always been considered separate from the symmetry breaking associated with inflation. (Of course, I wouldn't be the slightest bit surprised to find that someone, somewhere, at sometime tried to tie the two together. The problem is that inflation seems to have occurred far earlier than the point when electroweak symmetry was broken, by the Higgs mechanism.)

As you say:

Anyway freezing etc is a phase change - the molecules spontaneously arrange themselves into a rigid structure as the temperature drops. But forget rigidity, it's the fact that the molecules take up a different and perfectly well-defined relationship with each other. ...

I think part of the problem is that there was more than one period, in the very early history of this universe, where such phase changes "must" have occurred (by present reckoning, of course): 1) The decoupling of gravity from other quantum fields, 2) the breaking of "grand unification" (the unification of all the quantum fields, often designated as GUT, for Grand Unification Theory), and 3) the electroweak symmetry breaking (involving the Higgs mechanism).

The more-or-less usual model, in modern Cosmology, as far as I know, has inflation occurring at the GUT symmetry breaking. Of course, it's certainly possible that there may have been an inflationary epic associated with the decoupling of gravity from the quantum fields, but that's even further from our ability to address in anything more than a "hand waiving" sort of manner.

Even the GUT symmetry breaking is beyond our ability to address in anything more concrete than some general, highly simplified "toy" models, since we don't even know what GUT fits this universe (or even if any of the proposed GUTs may work).

Now, as to how any such "would cause the universe to inflate", well, General Relativity does provide a reasonable framework for modeling various Cosmologies, where one has different mixes of matter, radiation, and various other "fields". There are models, with appropriate combinations of matter, radiation, and other (sufficiently simple) fields where one is able to "blow space up like a balloon."

Of course, since there are so many other unknowns, even if the GUT symmetry breaking takes place in an epic where General Relativity is applicable, one cannot definitely say "we know why and how".

Now, as to how any such "would cause the universe to inflate", well, General Relativity does provide a reasonable framework for modeling various Cosmologies, where one has different mixes of matter, radiation, and various other "fields". There are models, with appropriate combinations of matter, radiation, and other (sufficiently simple) fields where one is able to "blow space up like a balloon."

When I said "I have no idea why this would cause the universe to inflate" I was not doubting that there are models, I was merely saying that I do not know anything about them. I am reminded of someone's lament (I can't remember who) that after five years of studying Greek and Latin at school, most pupils emerge with no knowledge beyond a profound conviction that such languages exist.

Some information on this was given in the Italian media, which provides some details on the cable error mentioned one month ago:http://www.televideo.rai.it/televideo/pub/articolo.jsp?id=11936
INFN president Ferroni said in an interview, that OPERA and LVD have compared the 2007-2008 data for cosmic muon neutrinos with those of 2008-2011, and found erroneous values due to a fibre optic malfunction. This discrepancy is compatible with the OPERA anomaly, and thus explaining it. So it's almost sure that the OPERA result wad due to a cable error.
So the recent ICARUS result is surely correct.

[This is a re-submission -- unaltered except for this note -- of the comment I submitted on Monday, April 02nd; which was then claimed to be "queued for moderation by site administrators" and to be "published after approval" as usual, but which since then has apparently neither been published nor explicitly disapproved. Please disregard this re-submission if the initial submission is still being queued or considered for publication. -- FW]

David Halliday wrote (03/30/12 | 13:03 PM):
> (By the way, your use of the term "indication" seems like it should be using the Einsteinian term "event". In your case, an event of observation by a particular participant. So long as that's what you mean by the term "indication", I'm OK with it.)

The word "event" is typically used not as referring to one particular participant ("at" one particular event) but to several participants (and even all participants imaginable) who would have met (passing each other) "at" this event.

For discussing geometric relations between certain participants, e.g. between A and B as we've been considering, I find the phrase "event Ej, as far as it pertains to participant A" more cumbersome than (the equivalent phrase) "indication Aj (of participant A)".

> By "BAj", do you mean the observation, by B [...], of the instance of this special class of "signal" emitted by A at "indication" "Aj"?

By "BAj" I mean B's indication of observing A's indication "Aj"; i.e. the first indication of B knowing about A's indication "Aj". (Recall that the participants under consideration are supposed to be capable of judging order or coincidence of their observations.)

And I mean no specification of this relation between participants A and B beyond A having stated the observable indication "Aj", B observing this, and being able to judge which other observations B collected coincidently with this observation of A's indication "Aj" (jointly being called B's indication "BAj") or which other observations B collected before or after.

If you insist on nevertheless calling this relation a ``special class of "signal"'' then any other ``class of "signal"'' would apparently have to involve some of B's indications other than (only) "BAj" along with "Aj". Such relations may well be called "(generalized) signal" under some circumstances, e.g. "signalling by exchanging chemicals", where the (first) indication of knowing that some "chemical" had been released is of quite negligible consequence compared to the (first) indication of actually holding on to that "chemical".

Now: do we agree that for A and B to evalute their distance between each other (in mutual agreement) the required duration(s) "[ABA]" of A is to be determined from a given indication "Aj" to A's first indication of knowing about B's first indication of knowing about "Aj"?

> [...] that a certain "participant" is occupying said "location", at least at some "time"

Unless you require that "locations" be considered which are not associated to (or identified by) certain identifiable participants (or even geometric relations to such "unidentified locations") we may well limit ourselves to considering the identifiable participants.

You said "The word 'event' is typically used not as referring to one particular participant ('at' one particular event)". That is true. That's why I expressed that I recognized that your use of the term "indication" was a restricted form of "event", one that occurred "at" "one particular participant".

However, you go on with "but [The word 'event' is typically used as referring] to several participants (and even all participants imaginable) who would have met (passing each other) 'at' this event." This is most certainly not true. On the other hand, the incorrectness of this statement of yours is not particularly consequential, at this time, at least.

Now, on to something that is far more consequential, and (potentially) problematic.

You state:

By "BAj" I mean B's indication of observing A's indication "Aj"; i.e. the first indication of B knowing about A's indication "Aj". (Recall that the participants under consideration are supposed to be capable of judging order or coincidence of their observations.)

Well, the potential problem with this "definition" is what you mean by "observing". In particular, B "observing A's indication 'Aj' ". How does B "observe" this? Is it by receiving an instance of that "special class of signal", sent from A to B, initiated at "A's indication 'Aj' "? Or by some other means?

The other far more likely to be problematic aspect is your stipulation that this is "the first indication of B knowing about A's indication 'Aj'." (Emphasis added)

Yeh, I've been seeing some other aspects of your contrived argument that try to "hide" little aspects that artificially attempt to exclude any "particle" (you insist that it must be a "participant" assigned all the capabilities and limitations of all other "participants") from arriving "first" (by defining the "fastest" "signal" to be "first"). Hence contriving a set of (non-physical) "definitions" such that any "superluminal" "particle" would be in violation of such "definitions".

What you are trying to pull here is no different than the "slight of hand" of a "magician", or a proof that 0=1 (or something similar), due to a similar "slight of hand".

Sorry, I'm not falling for such tricks.

For instance, you try to get me to agree with:

Now: do we agree that for A and B to evalute their distance between each other (in mutual agreement) the required duration(s) "[ABA]" of A is to be determined from a given indication "Aj" to A's first indication of knowing about B's first indication of knowing about "Aj"?

By defining these in terms of "first indication of knowing about"—regardless of what the nature of the "signal" is, or otherwise, of the nature of this "first indication of knowing about"—is just setting up a "hat trick".

Maybe it's time for me to be doing the definitions. I promise not to use "coordinates", or "events" that are not "at one particular participant", no "indistinguishable" "particles"/"signals"/etc. However, I will insist that there is one single special class of "signal" for which we have, as you stated,

the value of "distance" of A and B to each other is"1/2 c [ABA]",where "c" is a literal constant (plainly the letter "c". Proceding to the definition of "speed" in terms of such a distance value and a certain duration value, "speed of light" is subsequently obtained as the value "1 c", or for short "c").

In addition, this "c" is completely independent of participants, or their physical relationship with respect to one another (at least so long as the interval [ABA] is non-zero, though that can be handled as a degenerate case).

The one single special class of "signal", with the above characteristics, shall be designated as "light". In designating it such, there is no implied quantum character, "polarization", etc., i.e. no "possibly accompanying 'baggage' (such as 'energy', 'momentum', 'stress', 'spin', 'charge', ...)", just the ability to send and receive distinguishable signals with the above "speed" characteristics.

The relationship of such intervals, above, among five or more such "participants" is "flat".* The "participants" remain "rigid" to one another, in that regardless of the initiation of a "round trip" interval, such as [ABA], the interval is always the same.* And no participant detects any non-inertial aspect of their own motion (for instance, accelerometers, placed upon such participants, detect no accelerations).

Not all "projectiles" need be "participants", in the sense of having all the attributes and limitations thereof. In this, we simply do not require a "projectile" "to be capable of judging order or coincidence of their observations", since we are not requiring a "projectile" to be able to make any "observations".

All "observations" of a participant will always be local to said "participant". We will never need to have non-local "observations", even though Einstein allowed such, via synchronized "armies" of observers. So we will not need to address issues of "simultaneity".

The fact is, we can answer the original question of whether "Einstein's [Special] Relativity" does or does not "rule out superluminal particles" with only two participants, "pitcher A" and "catcher B", a few "projectiles" (we can be frugal, and, in a sense, "reuse" a single "projectile"), and the ability to send and receive as many distinguishable instances as desired of these "light" signals.

Is this acceptable to you? Is there anything else that we agreed upon, already, that you feel needs to be refreshed?

You see, unlike your extra, non-physical conditions such as requiring all "projectiles" to be "participants", complete with being "capable of judging order or coincidence of their observations", or that the "first" "signal" must be the one with the characteristic speed "c", are most certainly not part of Einstein's Special Theory of Relativity, but are extra contrivances designed for the sole purpose of "defining" certain things "away".

David

* Note: Not "ratios of", but the intervals themselves (any uniform scaling, such as conversion to some particular units, whether "time" like or "distance" like, does not change this).

David Halliday wrote (04/05/12 | 16:30 PM):
> [...] what you mean by "observing".

If "observing" is not admissible as axiomatic notion -- which notions would you suggest for trying to express what's meant by "that"?
(E.g. for expressing "what" you've been doing with my comments to enable you writing comments in reply; or likewise "what" has been or might be done with your comments in turn.)

> [...] your stipulation that this is "the first indication of B knowing about A's indication 'Aj'." (Emphasis added)

At least there seems no question what is meant by this stipulation (namely to consider just these pairs of indications, primarily, if not exclusively, for subsequently deriving geometric relations between A and B and the requisit additional participants; instead of any other pairs of indications).

> Maybe it's time for me to be doing the definitions. [...] I will insist that there is one single special class of "signal" for which we have, as you stated [a certain role in defining what's meant by (i.e. how to evaluate) "distance"]

When you write "for which we have" -- do you mean it (as I did) in the sense of having a certain role subsequent to being selected or classified?
Or (instead) in the sense of having a condition (or an additional condition) for how to select or classify in the first place?
Do you suppose a definition for the notion "distance" separate from the one (IMHO also Synge's and Einstein's) discussed above? ...

> I promise not to use "coordinates", or "events" that are not "at one particular participant" [...] The "participants" remain "rigid" to one another, in that regardless of the initiation of a "round trip" interval, such as [ABA], the interval is always the same. [...]

"Interval" (symbol "s") usually refers to a value assigned to a pair of events; and given (distinct) pairs of events which have the same "interval" value (a.k.a. pairs which are called "equal" by this measure) and such that at least one participant took part in all these events then the durations of this participant between its corresponding pairs of indications are not necessarily the same.

> And no participant detects any non-inertial aspect of their own motion (for instance, accelerometers, placed upon such participants, detect no accelerations).

"Accelerometer" -- isn't that a set of (at least) five distinguishable participants who determine the (ratios of) signal roundtrip durations between each other such that the corresponding Cayley-Menger-Determinant can be evaluated (provided they also find having remained rigid to each other)?

> we simply do not require a "projectile" "to be capable of judging order or coincidence of their observations", since we are not requiring a "projectile" to be able to make any "observations".

Certain observations not being required or considered for certain evaluations doesn't preclude them from being collected nevertheless. However, your proposal then apparently doesn't involve evaluation of any duration of the projectile, such as its duration from its indication of meeting (leaving) pitcher A to its indication of meeting (reaching) catcher B.
(When you were earlier (03/26/12 | 17:12 PM) referring to a procedure for determining the (average) "speed" of any other "projectile P" that is "thrown" from "pitcher A" and "caught" by "catcher B" without any need for defining any procedure for determining simultaneity I had been expecting this duration of the projectile to have a role.)

> All "observations" of a participant will always be local to said "participant".

Observations are attributed separately to individual distinguishable participants. (Surely this is an idealization which is essential to RT.)

> We will never need to have non-local "observations", even though Einstein allowed such, via synchronized "armies" of observers.

Like Einstein (and Synge) we'll have to consider certain sets of observers/participants; in particular a (or any) certain set with members A and B.
Does this have any bearing on observations collected by A (e.g. of indications stated by B) being separate from observations collected by B (e.g. of indications stated by A)?

> So we will not need to address issues of "simultaneity".

???
What exactly do you suppose to "go into the denominator" when trying to evaluate "speed"?

> you go on with "but [The word 'event' is typically used as referring] to several participants (and even all participants imaginable) who would have met (passing each other) 'at' this event." This is most certainly not true.

This remark I find very puzzling, too; perhaps you can resolve this when discussing your use of "interval" (instead of "duration" or "distance") above.

"Observing" is only "admissible as [an] axiomatic notion" if one defines what one means by an "observation". In Einstein's case, he permitted "observations" to be at locations other than local to the observer. However, to do so, he had to specify "simultaneity".

As I have already said:

All "observations" of a participant will always be local to said "participant". We will never need to have non-local "observations", even though Einstein allowed such, via synchronized "armies" of observers. So we will not need to address issues of "simultaneity".

See, I have defined what I mean.

So, going on...

I see you got "hung up" on my use of the word "interval". (This is especially interesting considering that my first use was in direct connection to your "[ABA]", as in "the interval [ABA]".)

"Interval" (symbol "s") usually refers to a value assigned to a pair of events; and given (distinct) pairs of events which have the same "interval" value (a.k.a. pairs which are called "equal" by this measure) and such that at least one participant took part in all these events then the durations of this participant between its corresponding pairs of indications are not necessarily the same.

Well, first off, this is completely applicable to my use of the term, here, especially when one includes the other definitions and stipulations I have provided (definition of observation, and no "events" that are not "at one particular participant", etc.). However, in order to avoid confusing you, simply substitute your word "duration" where I used "interval". So, we have

In addition, this "c" is completely independent of participants, or their physical relationship with respect to one another (at least so long as the [duration] [ABA] is non-zero, though that can be handled as a degenerate case).

...

The relationship of such [durations], above, among five or more such "participants" is "flat".* The "participants" remain "rigid" to one another, in that regardless of the initiation of a "round trip" [duration], such as [ABA], the [duration] is always the same.* And no participant detects any non-inertial aspect of their own motion (for instance, accelerometers, placed upon such participants, detect no accelerations).

...

* Note: Not "ratios of", but the [durations] themselves (any uniform scaling, such as conversion to some particular units, whether "time" like or "distance" like, does not change this).

Is that acceptable, now?

OK. Back to where you responded to my stipulations/definitions

Maybe it's time for me to be doing the definitions. ... I will insist that there is one single special class of "signal" for which we have, as you stated,

the value of "distance" of A and B to each other is"1/2 c [ABA]",where "c" is a literal constant (plainly the letter "c". Proceding to the definition of "speed" in terms of such a distance value and a certain duration value, "speed of light" is subsequently obtained as the value "1 c", or for short "c").

with:

When you write "for which we have" -- do you mean it (as I did) in the sense of having a certain role subsequent to being selected or classified?Or (instead) in the sense of having a condition (or an additional condition) for how to select or classify in the first place?Do you suppose a definition for the notion "distance" separate from the one (IMHO also Synge's and Einstein's) discussed above? ...

I used your own statement, as quoted, as a condition upon this one single special class of "signal"—the condition (along with the paragraph that followed) that actually allows this one single special class of "signal" to actually be used in this "certain role" ("subsequent to being selected [and] classified") of being used to define the above "distance".

After all, if one were to use some other "signal" in this same way, to define a "distance", one would get a different "distance" as a result!

No, this is not circular. Nor are we using some other means for determining "distance". What we are saying is that the definition of "distance" is based upon the characteristics of this one single special class of "signal", and no other concept of "signal".

OK. On to your "trouble" with the term "accelerometer", namely:

"Accelerometer" -- isn't that a set of (at least) five distinguishable participants who determine the (ratios of) signal roundtrip durations between each other such that the corresponding Cayley-Menger-Determinant can be evaluated (provided they also find having remained rigid to each other)?

Not necessarily. One could use any of a number of devices: Stain gauges, ring lasers, etc.

If you can prove that what you have is equivalent to an accelerometer, local to a single participant, then, yes, it would be admissible as an accelerometer.

Moving on...

To my statement that "we simply do not require a 'projectile' 'to be capable of judging order or coincidence of their observations', since we are not requiring a 'projectile' to be able to make any 'observations' "; you responded (in part) with:

Certain observations not being required or considered for certain evaluations doesn't preclude them from being collected nevertheless. ...

I absolutely agree. However, such "observations" are also not required to have an "order or coincidence" that corresponds in some simple direct way to those of our "participants".

You then continue with:

... However, your proposal then apparently doesn't involve evaluation of any duration of the projectile, such as its duration from its indication of meeting (leaving) pitcher A to its indication of meeting (reaching) catcher B.(When you were earlier (03/26/12 | 17:12 PM) referring to a

procedure for determining the (average) "speed" of any other "projectile P" that is "thrown" from "pitcher A" and "caught" by "catcher B" without any need for defining any procedure for determining simultaneity

I had been expecting this duration of the projectile to have a role.)

Well, in a sense, you are correct that the procedure "doesn't involve evaluation of any duration of the projectile, such as its duration from its indication of meeting (leaving) pitcher A to its indication of meeting (reaching) catcher B". Certainly not from the perspective of the projectile (so, the duration the "projectile" would "measure").

The fact is that we can obtain the (average) "speed" of any "projectile P" that is "thrown" from "pitcher A" and "caught" by "catcher B", as a ratio with that of the one single special class of "signal", without actually determining "any duration of the projectile, such as its duration from its indication of meeting (leaving) pitcher A to its indication of meeting (reaching) catcher B" from any participant, as well.

OK. To my specifying that "All 'observations' of a participant will always be local to said 'participant' " (as I restated at the beginning of this message), you add:

Observations are attributed separately to individual distinguishable participants. (Surely this is an idealization which is essential to RT.)

I quite agree. Actually, this is neither an idealization, nor is this only essential to Einstein's Special Relativity ("RT", as you stated). To do otherwise is an "idealization", and one that involves additional assumptions, or work to show it as being so reducible.

To my statement: We will never need to have non-local "observations", even though Einstein allowed such, via synchronized "armies" of observers. You initially responded with:

Like Einstein (and Synge) we'll have to consider certain sets of observers/participants; in particular a (or any) certain set with members A and B. ...

Yes, "a (or any) certain set with members A and B." However, our "certain set" will be far simpler, with no need to involve other participants besides "A and B". Simpler is better. ;)

You then continue by asking:

... Does this have any bearing on observations collected by A (e.g. of indications stated by B) being separate from observations collected by B (e.g. of indications stated by A)?

Absolutely! "Observations collected by A (e.g. of indications stated by B)" are "separate from observations collected by B (e.g. of indications stated by A)". As I have stated, "All 'observations' of a participant will always be local to said 'participant' ", and, as you added, "Observations are attributed separately to individual distinguishable participants."

To my statement "So we will not need to address issues of 'simultaneity' ", you act eminently confused, and respond with:

???What exactly do you suppose to "go into the denominator" when trying to evaluate "speed"?

Well, if you can't figure that out, yet, then I guess you'll just have to wait until we get all the preliminary definitions and stipulations out of the way. ;)

As for your last "issue", and the puzzlement you expressed, I'm afraid I will not be addressing that, since it involves things we simply won't be needing. Perhaps as a separate thread, once this is all done?

David Halliday wrote (04/15/12 | 20:58 PM):
> [...] After all, if one were to use some other "signal" in this same way, to define a "distance", one would get a different "distance" as a result!

Do you mean that's an absurdity (and therefore at least one of the premises were false)? Hardly:

If participants were to consider their (mutual) first observations which are "sufficiently chemical" for determining geometric relations between each other,
or their (mutual) first observations which are "sufficiently loud",
instead of their (mutual) first observations (plainly; devoid of any further requirements)
then these geometric relations of the same participants in the same trial are of course not necessarily equal.

Obviously ratios of "chronometric distances by chemical signalling" can and must be distinguished from ratios of "chronometric distances by sound signalling" and from ratios of "chronometric distances by light signalling".

However, defining additional requirements (such as "chemicality" or "loudness") generally requires some notion of geometric relations from the outset, which by default can be provided by evaluating the plain (mutual) first observations.

> "Observing" is only "admissible as [an] axiomatic notion" if one defines what one means by an "observation"

Looks like we don't even agree (in terms of terminology) that an "axiomatic notion" is precisely not the result of any definition, but rather an ingredient which is employed and required to express definitions (of notions other than the axiomatic ones).

For instance, since you've been using the phrases "one defines" and "one means": Would you (also) require that one defines what one means by those phrases?

And more specificly concerning the notion "observing":
Do you regard "defining" or "meaning" as solitary, solipsistic exercises?
Or is there some consideration of others involved (à la "We must be able to tell our friend ...")?

> I see you got "hung up" on my use of the word "interval". (This is especially interesting considering that my first use was in direct connection to your "[ABA]", as in "the interval [ABA]".)

I had noticed that you, while commenting on "my definition" in terms of "duration ratios", were rather indiscriminately referring to "intervals" as well. (Cmp. 03/26/12 | 17:40 PM and thereabouts.)

> Well, first off, this is completely applicable to my use of the term, here, especially when one includes the other definitions and stipulations I have provided

The equivalence in the particular case under consideration follows (also) from the definitions and stipulations concerning "rigidity" and "flatness" I indicated above. (That's why I didn't bother to press the case when I first observed your imprecision.)
What I'm hung up about, though, is that these requisite definitions and stipulations cannot presuppose in turn values of intervals (except "Null intervals", of course), but at most duration ratios.

> "accelerometer" [...] One could use any of a number of devices: St[r]ain gauges

How should be determined whether (or to which accuracy) some given device gauges/indicates values of "strain", at least in principle, unless it is sometimes (and this means in terms of though-experiments just as well permanently) calibrated by a Synge-Five-Point-Curvature-Meter?

> ring lasers

Sure. How many distinct identifiables (at least) make up a suitable "ring laser"; and which evaluation operation are they supposed to apply to their (mutually) collected observations, to distinguish (and discard) trials with "non-inertial motion" from the remaining ("valid") trials?

> If you can prove that what you have is equivalent to an accelerometer

... Isn't the burden of proof on you, or rather obligation to provide a definition which "We can tell our friends"? ...

> local to a single participant

Well -- if I'm writing of several, say five, distinct identifiable participants I'm not thinking of only a single such participant. Are you??
(So best drop that curious "local" phrase from your definition; either for being superfluous, or else for being irreproducible.)

> [...] no need to involve other participants besides "A and B". Simpler is better.

What's A going to be observing regarding only B except
"for a given indication of mine I've observed B's indication of having first observed it";
and vice versa B regarding only A?
Which evaluations might possibly applied to these utterly primitive observations in order to obtain measurements of the stipulations ("inertial motion" or whatever) you require?

In other words: can you make a useful "ring laser" of only two distinct parts??

Why did you violate the decency of posting your replay actually as a Reply? If you had actually done the decent thing and used the "Reply to This >>" link, as we have discussed before, I would have known about this reply of yours days ago.

Perhaps you wanted to try to "slip" this past me? Mr. "http://www.science20.com/ping_parlor/blog/such.a.constant.chore". (Yes, I know of your use of the URL entry to have your little sub-comments.)

Based upon your comments, I do wonder whether you wanted me not to notice.

OK. On to your comments:

You begin with your reply to me pointing out that "After all, if one were to use some other 'signal' in this same way, to define a 'distance', one would get a different 'distance' as a result!" You say:

Do you mean that's an absurdity (and therefore at least one of the premises were false)? Hardly:

If participants were to consider their (mutual) first observations which are "sufficiently chemical" for determining geometric relations between each other,or their (mutual) first observations which are "sufficiently loud",instead of their (mutual) first observations (plainly; devoid of any further requirements)then these geometric relations of the same participants in the same trial are of course not necessarily equal.

Obviously ratios of "chronometric distances by chemical signalling" can and must be distinguished from ratios of "chronometric distances by sound signalling" and from ratios of "chronometric distances by light signalling".

However, defining additional requirements (such as "chemicality" or "loudness") generally requires some notion of geometric relations from the outset, which by default can be provided by evaluating the plain (mutual) first observations.

First, what I stated is a simple point of fact. Furthermore, as you point out (apparently in agreement), one would then need to designate the nature of such (other) "distance" measures.

However, a fortiori, yes, the use of any signal other than the one which satisfies the criteria laid out is a violation of one or more of the premises. (Not that the premiss is "false", just that the premis is violated by that particular choice.)

Remember, the criteria (emphasis added, again):

... I will insist that there is one single special class of "signal" for which we have, as you stated,

the value of "distance" of A and B to each other is"1/2 c [ABA]",where "c" is a literal constant (plainly the letter "c". Proceding to the definition of "speed" in terms of such a distance value and a certain duration value, "speed of light" is subsequently obtained as the value "1 c", or for short "c").

In addition, this "c" is completely independent of participants, or their physical relationship with respect to one another (at least so long as the interval [ABA] is non-zero, though that can be handled as a degenerate case).

The one single special class of "signal", with the above characteristics, shall be designated as "light". In designating it such, there is no implied quantum character, "polarization", etc., i.e. no "possibly accompanying 'baggage' (such as 'energy', 'momentum', 'stress', 'spin', 'charge', ...)", just the ability to send and receive distinguishable signals with the above "speed" characteristics.

In any form of "spacetime" there can be no more than one single special class of "signal" that satisfies the stated condition on "c", or have you not noticed that in your studies, yet?

In Euclidean "spacetime" there are no classes of "signal" that satisfy this condition. In Newtonian/Galilean "spacetime" only "infinite" "speed" "signals" satisfy this condition. In Einsteinian/Minkowskian "spacetime" there is also only one such special "signal": It is one of the two principle premises of Einstein's Special Theory of Relativity. (Surely you know that, don't you?)

Additionally, your attempt to stipulate that we proceed strictly "by evaluating the plain (mutual) first observations" is a blatant case of the "begging the question" logical fallacy! After all, the question we are trying to address is "whether 'Einstein's [Special] Relativity' does or does not 'rule out superluminal particles' ". (Of course, perhaps that has been your intent?)

So this stipulation will most definitely have to be eliminated!

On the issue of whether "observation" is admissible as an "axiomatic notion"... Since, if there is potential disagreement about what is meant by a possible "axiomatic notion", such as "observation", as there appears to be with us, then one must define what one means by that notion, such as an "observation". So, no, "observation" does not appear to be admissible as an "axiomatic notion" in our discussion.

Of course, this is just as Einstein did, in his Special Theory of Relativity. He did not treat the notion of "observation" as an "axiomatic notion". He recognized that it needed to be strictly defined, in order to be properly used.

You then state "What I'm hung up about, though, is that these requisite definitions and stipulations cannot presuppose in turn values of intervals (except 'Null intervals', of course), but at most duration ratios." Now, are you using "interval" here in the general sense, of arbitrary spacetime intervals between arbitrary spacetime points? If so, then yes, we have most certainly not amassed sufficient "requisite definitions and stipulations" to do so. However, we simply don't need to do so in order to answer the question we are addressing: Whether "Einstein's [Special] Relativity" does or does not "rule out superluminal particles".

Additionally, while we do have sufficient "requisite definitions and stipulations" to "presuppose" that "durations" actually have "values" (even if they may be zero), it is true that we don't have sufficient to determine any actual values (since that would require additional information about the relative positions of the "participants" that we cannot obtain independent of our "requisite definitions and stipulations"). However, as you say, we can determine the "values" (in a relative way) of the "ratios" of such "intervals", and that is sufficient for our needs.

When I pointed out that we would have "no need to involve other participants besides 'A and B'. Simpler is better", you responded with:

What's A going to be observing regarding only B except"for a given indication of mine I've observed B's indication of having first observed it";and vice versa B regarding only A?Which evaluations might possibly applied to these utterly primitive observations in order to obtain measurements of the stipulations ("inertial motion" or whatever) you require?

Do you not remember that I stipulated a distinction between "participants", and other "things" such as "projectiles"?

I'll ignore your fixation on "ring lasers", since that was only provided as one example of many of the concept of an "accelerometer". After all, I most definitely expect that the notion of an "accelerometer" satisfies the "obligation to provide a definition which 'We can tell our friends' " far better than "a set of (at least) five distinguishable participants who determine the (ratios of) signal roundtrip durations between each other such that the corresponding Cayley-Menger-Determinant can be evaluated (provided they also find having remained rigid to each other)".

Besides, since you were the one that brought up the latter, you are the one that is under obligation to "prove" that it satisfies the requirements and functionality of an "accelerometer" (a very general, and far more generally understood concept and functionality).

Now, I asked "Is that acceptable, now?" However, your responses suggest otherwise. Is that an incorrect assessment?

Remember that the initial part of the text you've been quoting (again, thanks) stems from my description of the chronometric light distance definition (03/22/12 | 18:48 PM); where (04/05/12 | 09:15 AM)
for A and B to evalute their distance between each other (in mutual agreement) the required duration(s) "[ABA]" of A is to be determined from a given indication "Aj" to A's first indication of knowing about B's first indication of knowing about "Aj".

If this is not the criterion you require -- then what instead?
Especially: which notion of "distance" instead the one I indicated?

Your only other criterion is apparently, as you stated and again emphasized:
> this "c" is completely independent of participants, or their physical relationship with respect to one another

As I had pointed out in the text you quoted: "c" is foremost a letter, and as such a matter of convention (to be adopted by the participants).
Anything further would depend on stipulations of what you mean by (how to measure) "distance" and "speed". Don't you suppose that there are quite specific conditions on the relations of A and B between each other and further participants for them to obtain any "speed" values?

> your attempt to stipulate that we proceed strictly "by evaluating the plain (mutual) first observations" is a blatant case of the "begging the question" logical fallacy! After all, the question we are trying to address is "whether 'Einstein's [Special] Relativity' does or does not 'rule out superluminal particles' ".

I surely didn't claim that the proof was very difficult, given the indicated (Synge's, and effectively Einstein's) chronometric distance definition.
But I was (tried to be) careful about pointing out, that the notion or values of "speed" are not used in the distance definition.
So there is actually something to be proven or derived about the http://en.wikipedia.org/wiki/Codomain of the quantity "speed" defined based on chronometric light distance.

> So this stipulation will most definitely have to be eliminated!

At least we seem agree that this stipulation is important.
And we might as well "split up the turf" of our disagreement along this distinction.
Are you suggesting that Einstein (Marconi?, Hertz?, ...) were not by default considering indications with plain first observations, but indications after those, or (even) indications before?

> In any form of "spacetime" there [...]

Unless you're referring here to "events without identifiable participants" (remember?) there are apparently an awful lot more distinct participant involved than just 2 ("A and B"); and so far that's fine with me.

What do you mean by "speed" there? (Together with which notion of "distance"?)

> In Einsteinian/Minkowskian "spacetime" there is also only one such special "signal": It is one of the two principle premises of Einstein's Special Theory of Relativity.

The principal premise of Einstein's Special Theory of Relativity (and likewise the GTR) is the notion of "time" of any given participant as "indication" (e.g. "of the small hand") of this participant. The rest are further stipulations based on that premise; in particular definitions of what's meant by (i.e. how to measure) "distance", "simultaneity", "speed".

> Do you not remember that I stipulated a distinction between "participants", and other "things" such as "projectiles"?

I have no idea how to reproduce such a stipulated distinction from the outset; but I remember having suggested to define the notions of "distance" and "speed" such that the distance value of A and B to each other as well as speed value at which A and B exchanged projectile P might be obtained without having to consider observations collected by projectile P and any judgements which P might make about these observations.

But observations collected and judgements rendered (about the own observations) are required from participants besides A and B; three more for determining the duration ratios needed in evaluating the Cayley-Menger-Determinant, and one participant as "middle between" A and B, for determining their "simultaneous" indication pairs, such that "speed of P" could be evaluated.

> since you were the one that brought up the [evaluation of Cayley-Menger-Determinants, as "Synge's Five Point Curvature Meter"], you are the one that is under obligation to "prove" that it satisfies the requirements and functionality of an "accelerometer"

I had pointed to the evaluation of Cayley-Menger-Determinants (between five participants in terms of their mutual ping duration ratios) as a condition for distinguishing "the special, flat case" of RT from "the general case" (see again 03/22/12 | 18:48 PM).
Subsequently I've sketched definitions of the chronometric light distance in "the special, flat case" and of "speed" based on that. A notion of "acceleration" would follow accordingly; and yes, "the special, flat case" Synge's "Curvature Meter" performs as a "Acceleration Meter", AFAIU.

But you brought up "accelerometer" as if it meant anything before you've even declared what you might mean by (i.e. how to measure) "distance" and "speed".

> Now, I asked "Is that acceptable, now?" However, your responses suggest otherwise. Is that an incorrect assessment?

I've tried to point out where I find your definitions unacceptable -- as representations of Einstein's RT, especially considering the urgent requirements which he expressed perhaps only after 1905.
And I still like to see what you mean (and/or what you think Einstein meant) by "speed".

p.s.
> Why did you violate the decency of posting your replay actually as a Reply?

Good grief! -- Sorry, I guess I'm just more used to "scienceblog"-style commenting; and I must have pasted my text in the "add a comment" editor box right underneath your comment, realizing the difference to a proper "Reply" only days later, when I found that my comment had been published. Glad you found it too, already, before I might have wondered ... and I try to be more careful about that now.

Are you suggesting that Einstein (Marconi?, Hertz?, ...) were not by default considering indications with plain first observations, but indications after those, or (even) indications before?

I am most certainly saying that they "were not by default considering indications with plain first observations"—most especially not Einstein (he knew better than the others you list that such is invalid, in general!)!

Now, in saying this, I most certainly am not saying that they (especially Einstein) were "considering" "indications after those [plain first observations], or (even) indications before". No, the question of whether the one special class of "signal" (namely light!) they were considering would be before or after any other "indications with plain first observations" was completely irrelevant!

If you think otherwise, then you have a great deal of relearning to do. (Or maybe a great deal of unlearning.)

Yes, this looks like a good place to concentrate our efforts, right now. :)

Sorry guys (David and Derek) I should point out that as you know I am a laywoman who is probably totally out of my depth here, I am quite confused about lots of things to do with physics and I'm worried that I might be wasting everyone's time even just answering your question as to what I thought or found troubling. Also I am pretty stressed at the moment, so I'm finding it difficult to concentrate properly on it all, this is unusual for me as I can normally concentrate easily on just about anything I want, to the exclusion of everything else but not now unfortunately.

So I hope you don't mind me trying to collect my thoughts by summarizing what was asked and answered more recently by David and Derek and also by me earlier on in the comments section.

So more recently David said :-

Of course, your answer, involving the deprecated "relativistic mass" concept, caused Helen some (understandable) difficulty, thus leading to her question concerning the labeling of the Higgs boson as the "God particle".

then Derek asked me :-

Helen - is this true? Would you have understood better if I had told you that not all energy has mass? I have started correcting my original replies as they were all wrong.

Of course, I cannot know with any degree of certainty what Helen actually thought, so I would amend what I said with "appears to have caused Helen some (understandable) difficulty", since all I can go by is what I see.

So, it's certainly good to check to see what Helen actually thought, or found troubling.

David

So my original question earlier in the comments section was to ask if Sascha was right when he claimed that :-

Energy is inert, inertia is expressed in terms of mass. Energy is NOT converted into mass ever. Energy can take the form of matter, but the mass is just the inertia of the black box which does not change when the electron and positron inside annihilate.

Or whether instead Lubos was right when he said :-

The conversion of one type of mass/energy to another is about moving the values from one term to another term in a particular decomposition of the total mass/energy into pieces....In the LHC rings, the protons are given what every sane person - i.e.. people not including you - call energy. It's obtained from the electric fields that accelerate the charged particles around the ring. The energy of a proton is now 4 TeV per proton. When these protons collide, they may create several or lots of top quarks or Higgs bosons which have the mass of 173 or 125 GeV/c^2....One may talk about "mass" and "energy" as two words for the very same quantity (or the same "kind" of a quantity) and that's how it's pretty much done in physics but those laymen can't swallow this identification - that was really my point....It's a completely standard science language to talk about mass being converted to energy or various forms of energy and vice versa, see e.g. these 2 million pages with preprints:

Then I asked if they could both somehow be right, or is it possible that no one really knows the answer for sure one way or the other yet? Then David explained that they were both right and both wrong :-

The principle way in which they are both wrong is in asserting that their description is the total answer, and that the other's description is what is incorrect.

Then I asked David the principle way that they were both correct and this is when I started rather pedantically asking a few times whether energy can be converted into mass or not?

Then David explained about Newtonian mechanics and the conservation of energy and momentum which I understood without any problem : -

The total of all energy (or momentum) before some interaction (or even a complex set of many interactions) will be the same as the total energy (or momentum) afterward.... and that there are multiple forms of energy: Kinetic (energy of motion), potential (stored mechanical potential to do work, such as potential energy in a stretched or compressed spring, or gravitational potential energy, etc.), chemical, etc. And, furthermore, the fact that the conservation of energy law only holds, in general, if all these myriad forms of energy are treated as equivalent, and added together to give the total energy.

Then David explained that Einstein's Special Theory of Relativity (SR), and his famous equation (derived therefrom): E = mc2 indicates that mass is also a "form" of energy.

In a sense, the "crux" of Sascha's and Lubos' arguments both stem from this one equation. Lubos retains the "form of" aspect, while Sascha, founded upon the realization that "c" (the speed of light in a vacuum), that is used in that equation, is "nothing but a conversion factor" between the units we call distance and the units we call time—hence, the c2 is "nothing but a conversion factor" between the units we call "mass" and the units we call "energy"—rightfully sees energy and mass as the same "thing". So, Sascha is completely correct when he says things like "c is a unit conversion constant, so what E = m c^2 is saying is basically E = m, i.e. they are one and the same". On the other hand, Lubos is well within the correct (historic) physics of accounting all forms of energy as being equivalent, while distinguishing them as being of various "types" or "forms".

Then I vaguely understood when David explained how the separate conservation laws of energy and momentum become merged into a single law of conservation of 4-momentum (energy-momentum). So, the total 4-momentum before will equal the total after any interaction. InitiallyI wasn't sure what 'p' stood for so I was quite happy when David said that there was a disagreement between the equations unless p = 0 but I should have asked, I assumed that p stood for a particle's momentum?

Couple this with the SR invariant where the square of the magnitude of the 4-momentum = E2 - p2 = m2 (in units where c=1, so such things don't distract), and one finds that this invariant mass will be the same before and after any interaction.

Now, you might notice that there is a disagreement between the first equation (which is Sascha's E = m, in these units) and this last equation (E2 - p2 = m2), unless p = 0. This is because the first equation is only strictly true when we are at rest with the center of mass (which is defined by the total p = 0), so we often append a zero subscript to that energy (E0), the rest energy.*

However, the second equation has universal applicability. In fact, it is what allows one to compare the mass of a box containing an electron and a positron, to the same box containing the two photons after the electron and positron have annihilated—as Sascha put it "the inertia of the black box which does not change when the electron and positron inside annihilate." Furthermore, while the inertia (inertial mass, or just mass) of the box is "defined" in the rest frame of that box, it is at rest with the center of mass of the box and its contents, so p = 0, and we can once again see E = m.

So, in this sense, the total mass (inertial mass, inertia) of the colliding, high energy protons does not change from before they collide to after they collide and a spray of new massive particles are created. On the other hand, the total mass has changed from the time when we had two protons, nearly at rest with each other, to the point where they have been accelerated to high energy just before the collision: The system has gained mass due to the injection of energy into the system, thus accelerating these two protons to high energy.

So, yes, energy can and has been converted into mass. (Of course, that energy came from some mass somewhere else, whether it came from the Sun loosing some mass, or from chemical reactions loosing some mass, or nuclei in a fission reactor loosing some mass, etc.)

The fact is, even just the absorption of a photon by an atom increases the mass of the (now excited) atom. However, the total mass of the photon plus atom system remains the same before the photon is absorbed to after it is absorbed, even though the invariant ("rest") mass of the photon is zero.

So yes I felt that I understood all of this explanation by David about how energy can appear to be converted into mass before and after the effects of momentum but then I started wondering why Tommaso and everyone else is always going on about where exactly the Higg's resides and the GEVs of 131 to 133 where iodine and tin reside in the periodic table etc. So I asked about the Higgs boson, field and mechanism and why do they call the Higg's boson the God particle? If all energy already has mass then there's nothing particularly amazing about the Higg's mechanism is there? Why all the 10 billion dollar fuss?

Then with regard to the Higgs family I had absolutely no difficulty understanding when Derek explained that :-

It's role in the early universe was a little more dramatic. The Higgs field we live in now could be likened to the solidified lava after a volcano has erupted. The God particle was responsible for the eruption itself :)At some point after the initial fluctuation, the state of the vacuum was only just stable, with a huge amount of energy available in the Higgs field. This then fell to a lower energy level, releasing the excess energy and, for reasons that are not altogether obvious, :) blowing space up like a balloon. So in that early epoch, it was basically making the universe as we know it. Hence its nickname. Unlike other versions of the deity it was not creating it ex nihilo but was converting the energy of "empty" space which was already there.

I interpreted this as meaning the energy of empty space was converted into mass by the Higg's field and that the Higg's or God particle somehow triggered it and that energy can be converted into mass by the Higgs field. Then Derek started going back through his other comments about the Higgs and changing them, so now I have to read these new comments since you asked me these questions to see if I'm more or less confused by them. Does that answer your questions? With regard to relativistic mass I am definitely confused but I can't read any more at present or my brain will explode.

Unfortunately, in physics we do have a number of different mass "thingies" (at least one of which has been deprecated, by most in relativistic physics): Inertial mass, gravitational mass, rest mass, invariant mass, "dynamical" or "dynamic" mass, relativistic mass, etc. Some of these "thingies" are identified with others, at least within the frameworks of certain theories. However, even when certain theories tag more than one of these as being identical, we physicists must maintain a certain degree of skepticism: Sufficient, at least, to allow for testing the degree of equivalence.

So, perhaps this subject simply isn't as simple as one may suppose, even for one that "knows the physics perfectly well".

Oh well that's a relief, there's certainly nothing simple about it all to me at present and to be honest I am still very confused but so what? I keep reminding myself that Einstein always said if you can't explain something in in physics to your grandma then you haven't understood it but maybe he was wrong, I'm not as bright as my Grandma I'm sure!

So, going back to your recent questions :-

Of course, your answer, involving the deprecated "relativistic mass" concept, caused Helen some (understandable) difficulty, thus leading to her question concerning the labeling of the Higgs boson as the "God particle".

then Derek asked me :-

Helen - is this true? Would you have understood better if I had told you that not all energy has mass? I have started correcting my original replies as they were all wrong.

Of course, I cannot know with any degree of certainty what Helen actually thought, so I would amend what I said with "appears to have caused Helen some (understandable) difficulty", since all I can go by is what I see.

So, it's certainly good to check to see what Helen actually thought, or found troubling.

David

I think that I can quite confidently say that I don't even understand your questions ha ha!!!

Please feel to delete this comment anyone that wants to! In my defence at least I did try to answer your questions :)

Yes. The 'p' was to designate momentum of the particle or system. I'm sorry I didn't make this explicit. (I think I assumed that it was understood, but assuming almost anything can easily bite one in the hiney.)

Please don't apologise David, I am extremely grateful for all the time and effort you and Derek have put into explaining these concepts to interested laypeople like me. BTW I didn't mean searching for the Higgs at GEV 133 I meant GEV 125 which just happens to be where the atomic mass 133 for iodine and tin etc. resides. I was getting tired. Now I'm refreshed after a good night's sleep, so I'm rereading all Derek's quite brilliant explanations about things I didn't understand for a long time, some of which he says he has rewritten and I will post here if there's anything that still find confusing, unless you don't think I should? I could go back to posting on my corkboard instead?

Well, already this thread on mass-energy equivalence is nothing to do with Tommaso's article :) Really it belongs under the Higgs mass article, hanging off Sascha and Lubos's dog-fight. I am seriously wondering whether there is a point in perhaps creating a blog of Layperson's Questions, not to teach and inform but to ask. Just an idea, I expect it will crash one way or another.

I am sorry if my last-minute alterations caused you confusion. I confess I was getting irritated with David insisting that "mass" should always mean an object's invariant mass - not the relativistic mass which everyone else seems to be able to talk about without blushing. I am now going to have to go around in sackcloth and ashes putting the record straight.

... I am seriously wondering whether there is a point in perhaps creating a blog of Layperson's Questions, not to teach and inform but to ask. ...

Perhaps a 'blog post with just a "rules of the road"—the rules for people to post layperson's questions, without expectation of receiving responses there, and, perhaps, some "rules" about what sorts of things will be subject to deletion—open to laypeople to simply post questions, that wouldn't, necessarily, be answered there, but could be taken up as separate "answer" posts?

Yes indeed. I'm open to suggestions! It would be nice to have a framework for both questions and answers. Even a special symbol when you decide to say something that is contentious in order to keep things simple. I'll give it a go this week, the worst result will be some wasted words. And a few summary executions.